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MuiButton-root MuiButton-text MuiButton-textPrimary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorPrimary MuiButton-root MuiButton-text MuiButton-textPrimary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorPrimary sc-d74559df-0 hctdIg css-ak4akz" tabindex="0" type="button" href="" target="_self"><span class="sc-b323b31-0 btXZGI button-label" display="inline-flex"><div width="16.5px" height="13px" class="sc-6293d692-0 eerUnR"><span display="block" height="2px" width="100%" opacity="1" transform="rotate(0)" class="sc-b323b31-0 fAyXOw"></span><span display="block" height="2px" width="100%" opacity="1" class="sc-b323b31-0 jYoQJr"></span><span display="block" height="2px" width="100%" opacity="1" transform="rotate(0)" class="sc-b323b31-0 bzvkpX"></span></div></span></button></div><ul width="100%" height="0px" class="sc-ace17a57-0 sc-f5e67a3c-2 girkTs czlhnZ"><div display="none" class="sc-ace17a57-0 bCtuFU"><a rel="" target="" width="100%" display="flex" href="/" class="sc-e69ac761-0 kTZeVj"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="130" height="30" decoding="async" data-nimg="1" class="sc-f5e67a3c-5 fcUGTU" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1683539914-logo.svg"/></div></a></div><div class="sc-ace17a57-0 cBRNHO"><li height="fit-content" width="100%" tabindex="0" class="sc-6293d692-0 hEIHLV"><div width="100%" class="sc-ace17a57-0 gbwWMz"><div height="fit-content" width="100%" class="sc-ace17a57-0 caCSrG"><span font-size="textXl" font-weight="medium" display="block" cursor="pointer" width="100%" class="sc-b323b31-0 kzoxAi">Products</span><div transform="rotateX(0deg)" class="sc-ace17a57-0 fxtsZN"><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 448 512" color="#A9A9AD" style="color:#A9A9AD" height="12" width="12" xmlns="http://www.w3.org/2000/svg"><path d="M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z"></path></svg></div></div></div><div pointer-events="none" class="sc-6293d692-0 sc-610ba7e0-0 fqJJID gkvAJG"><div class="sc-ace17a57-0 iIvmda"><div class="sc-ace17a57-0 fXUJvn"><div class="sc-ace17a57-0 jbARwL"><div class="sc-ace17a57-0 eFYjSa"><div class="sc-ace17a57-0 gYFcFc"><span display="block" width="auto" class="sc-b323b31-0 gIJLbd">APIs</span></div><div class="sc-ace17a57-0 eTCxuy"><div class="sc-ace17a57-0 ldsYPN"><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC bGaVbc"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/product/voice-agent-api"><div class="sc-ace17a57-0 gCajMv"><div class="sc-ace17a57-0 sc-3618c394-4 ftcNci bpvjgx"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060023-speech-to-speech.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dVEgqo">Voice Agent API</span><span font-size="textXs" class="sc-b323b31-0 sc-3618c394-14 lnJhVG cFsKfJ">For real-time AI Agents</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC bGaVbc"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/product/text-to-speech"><div class="sc-ace17a57-0 gCajMv"><div class="sc-ace17a57-0 sc-3618c394-4 ftcNci bpvjgx"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060055-text-to-speech.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dVEgqo">Text to Speech API</span><span font-size="textXs" class="sc-b323b31-0 sc-3618c394-14 lnJhVG cFsKfJ">Responsive, natural-sounding voices</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC bGaVbc"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/product/speech-to-text"><div class="sc-ace17a57-0 gCajMv"><div class="sc-ace17a57-0 sc-3618c394-4 ftcNci bpvjgx"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060077-speech-to-text.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dVEgqo">Speech to Text API</span><span font-size="textXs" class="sc-b323b31-0 sc-3618c394-14 lnJhVG cFsKfJ">Unmatched accuracy, speed & cost</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC bGaVbc"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/product/audio-intelligence"><div class="sc-ace17a57-0 gCajMv"><div class="sc-ace17a57-0 sc-3618c394-4 ftcNci bpvjgx"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060103-brain-ai.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dVEgqo">Audio Intelligence API</span><span font-size="textXs" class="sc-b323b31-0 sc-3618c394-14 lnJhVG cFsKfJ">Powered by AI Language models</span></div></div></a></div></div></div></div></div></div><div width="calc(100%)" class="sc-ace17a57-0 sc-3618c394-6 hiDOHk juEUpi"><div width="100%" class="sc-ace17a57-0 lePzZD"><span display="block" height="36px" class="sc-b323b31-0 ilnsGr">Announcements</span><style data-emotion="css 1y3y2u2">.css-1y3y2u2{font-family:var(--font-inter, sans-serif);font-size:1.0446428571428572rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:4px 5px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms 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MuiButton-colorSecondary MuiButton-root MuiButton-text MuiButton-textSecondary MuiButton-sizeSmall MuiButton-textSizeSmall MuiButton-colorSecondary sc-d74559df-0 fqnlbI sc-6e03a9e4-0 iumJHL sc-3618c394-0 gxydGy css-6n9fb7" tabindex="0" type="button" __typename="ComponentCallToActionRecord" id="Xho9X9_YQj2HBRVr87BG0g" href="/learn?type=Article&page=1&category=Announcements"><span class="sc-b323b31-0 fcPowg button-label" display="inline-flex"><span>View more</span></span><style data-emotion="css kcxyz4">.css-kcxyz4{display:inherit;margin-right:-2px;margin-left:8px;}.css-kcxyz4>*:nth-of-type(1){font-size:18px;}</style><span class="MuiButton-icon MuiButton-endIcon MuiButton-iconSizeSmall css-kcxyz4"><div width="fit-content" class="sc-ace17a57-0 ddioGD"><span display="inline-flex" class="sc-b323b31-0 bZmEHx"><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 448 512" height="16" width="16" xmlns="http://www.w3.org/2000/svg"><path d="M438.6 278.6c12.5-12.5 12.5-32.8 0-45.3l-160-160c-12.5-12.5-32.8-12.5-45.3 0s-12.5 32.8 0 45.3L338.8 224 32 224c-17.7 0-32 14.3-32 32s14.3 32 32 32l306.7 0L233.4 393.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l160-160z"></path></svg></span></div></span></a></div><div class="sc-ace17a57-0 gzWdaa"><a rel="" target="" display="-webkit-box" height="100%" width="100%" class="sc-e69ac761-0 ecplwP sc-2850a57f-3 cPKdIq" href="/learn/introducing-nova-3-speech-to-text-api"><div width="100%" height="100%" id="e1wy33mNTlGk8-WqDH28_Q" class="sc-ace17a57-0 sc-2850a57f-1 fJWxEy ggobuO"><div width="100%" height="150px" class="sc-6293d692-0 eWcIvK"><div class="sc-ace17a57-0 sc-5f7d928-0 fvbMGK image-wrapper" width="100%" height="100%"><img alt="Introducing Nova-3: Setting a New Standard for AI-Driven Speech-to-Text" loading="lazy" width="590" height="259" decoding="async" data-nimg="1" class="sc-2850a57f-2 dSsmQU" style="color:transparent;object-fit:cover" srcSet="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1740086862-2502-nova-3-blog-header.jpg%3Fauto%3Dformat%26w%3D590&w=640&q=75 1x, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1740086862-2502-nova-3-blog-header.jpg%3Fauto%3Dformat%26w%3D590&w=1200&q=75 2x" src="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1740086862-2502-nova-3-blog-header.jpg%3Fauto%3Dformat%26w%3D590&w=1200&q=75"/></div></div><div class="sc-ace17a57-0 biWqHE"><span font-weight="semiBold" class="sc-b323b31-0 iNRMrC"><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 320 512" color="#ffffff" class="sc-2850a57f-0 Tcnof" style="color:#ffffff" height="12" width="12" xmlns="http://www.w3.org/2000/svg"><path d="M285.476 272.971L91.132 467.314c-9.373 9.373-24.569 9.373-33.941 0l-22.667-22.667c-9.357-9.357-9.375-24.522-.04-33.901L188.505 256 34.484 101.255c-9.335-9.379-9.317-24.544.04-33.901l22.667-22.667c9.373-9.373 24.569-9.373 33.941 0L285.475 239.03c9.373 9.372 9.373 24.568.001 33.941z"></path></svg>Introducing Nova-3: Setting a New Standard for AI-Driven Speech-to-Text</span><span class="sc-b323b31-0 jUNaqu">Published on 02/12/25</span></div></div></a></div></div></div></div></li><li height="fit-content" width="100%" tabindex="0" class="sc-6293d692-0 hEIHLV"><div width="100%" class="sc-ace17a57-0 gbwWMz"><div height="fit-content" width="100%" class="sc-ace17a57-0 caCSrG"><span font-size="textXl" font-weight="medium" display="block" cursor="pointer" width="100%" class="sc-b323b31-0 kzoxAi">Solutions</span><div transform="rotateX(0deg)" class="sc-ace17a57-0 fxtsZN"><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 448 512" color="#A9A9AD" style="color:#A9A9AD" height="12" width="12" xmlns="http://www.w3.org/2000/svg"><path d="M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z"></path></svg></div></div></div><div pointer-events="none" class="sc-6293d692-0 sc-610ba7e0-0 fqJJID gkvAJG"><div class="sc-ace17a57-0 iIvmda"><div class="sc-ace17a57-0 fXUJvn"><div class="sc-ace17a57-0 jbARwL"><div class="sc-ace17a57-0 exshrD"><div class="sc-ace17a57-0 gYFcFc"><span display="block" width="auto" class="sc-b323b31-0 gIJLbd">Use Cases</span></div><div class="sc-ace17a57-0 eTCxuy"><div class="sc-ace17a57-0 ldsYPN"><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/solutions/contact-centers"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060222-customer-service.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Contact Centers</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/solutions/medical-transcription"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060247-medical.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Medical Transcription</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/deepgram-for-voicebots-and-chatbots"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060265-conversational-ai.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Conversational AI</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/solutions/speech-analytics"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060282-speech-analytics.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Speech Analytics</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" target="" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe" href="/solutions/media-transcription"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060298-media.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Media Transcription</span></div></div></a></div></div></div></div><div class="sc-ace17a57-0 bcBFEg"><a rel="" target="" class="sc-e69ac761-0 bkHGsI sc-3618c394-11 cTfqJK" href="/customers"><div class="sc-ace17a57-0 ldePaW"><div width="28px" height="28px" class="sc-6293d692-0 sc-3618c394-1 ipShUF kXFUqt"><div class="sc-ace17a57-0 sc-5f7d928-0 fvbMGK image-wrapper" width="100%" height="100%"><img alt="Customers" loading="lazy" width="16" height="16" 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fxtsZN"><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 448 512" color="#A9A9AD" style="color:#A9A9AD" height="12" width="12" xmlns="http://www.w3.org/2000/svg"><path d="M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z"></path></svg></div></div></div><div pointer-events="none" class="sc-6293d692-0 sc-610ba7e0-0 fqJJID gkvAJG"><div class="sc-ace17a57-0 iIvmda"><div class="sc-ace17a57-0 fXUJvn"><div class="sc-ace17a57-0 jbARwL"><div class="sc-ace17a57-0 exshrD"><div class="sc-ace17a57-0 gYFcFc"><span display="block" width="auto" class="sc-b323b31-0 gIJLbd">Resources</span></div><div class="sc-ace17a57-0 eTCxuy"><div class="sc-ace17a57-0 ldsYPN"><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a rel="" 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alt="Transcription Tool" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" class="sc-3618c394-8 jzJMzZ" style="color:transparent;object-fit:cover" src="https://www.datocms-assets.com/96965/1728060712-transcription.svg"/></div></div><span font-size="textSm" class="sc-b323b31-0 sc-3618c394-15 fmcyDO gpxdfo">Transcription Tool</span></div></a></div></div></div></div></div></li><li height="fit-content" width="100%" tabindex="0" class="sc-6293d692-0 hEIHLV"><div width="100%" class="sc-ace17a57-0 gbwWMz"><div height="fit-content" width="100%" class="sc-ace17a57-0 caCSrG"><span font-size="textXl" font-weight="medium" display="block" cursor="pointer" width="100%" class="sc-b323b31-0 kzoxAi">Developers</span><div transform="rotateX(0deg)" class="sc-ace17a57-0 fxtsZN"><svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 448 512" color="#A9A9AD" style="color:#A9A9AD" height="12" width="12" xmlns="http://www.w3.org/2000/svg"><path d="M207.029 381.476L12.686 187.132c-9.373-9.373-9.373-24.569 0-33.941l22.667-22.667c9.357-9.357 24.522-9.375 33.901-.04L224 284.505l154.745-154.021c9.379-9.335 24.544-9.317 33.901.04l22.667 22.667c9.373 9.373 9.373 24.569 0 33.941L240.971 381.476c-9.373 9.372-24.569 9.372-33.942 0z"></path></svg></div></div></div><div pointer-events="none" class="sc-6293d692-0 sc-610ba7e0-0 fqJJID gkvAJG"><div class="sc-ace17a57-0 iIvmda"><div class="sc-ace17a57-0 fXUJvn"><div class="sc-ace17a57-0 jbARwL"><div class="sc-ace17a57-0 exshrD"><div class="sc-ace17a57-0 eTCxuy"><div class="sc-ace17a57-0 ldsYPN"><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a href="https://developers.deepgram.com/documentation/" rel="noreferrer noopener" target="_blank" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" 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src="https://www.datocms-assets.com/96965/1728060860-tutorials.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 sc-3618c394-13 hHDluE dRVqCB">Tutorials</span></div></div></a></div><div width="max-content" class="sc-ace17a57-0 sc-3618c394-5 dMJoKC kjWGMU"><a href="https://status.deepgram.com/" rel="noreferrer noopener" target="_blank" text-decoration="none" class="sc-e69ac761-0 cCnzAI sc-3618c394-10 jycipe"><div class="sc-ace17a57-0 ljypZA"><div class="sc-ace17a57-0 sc-3618c394-4 iNSltq iIhisP"><div class="sc-ace17a57-0 sc-5f7d928-0 iMdtXa kritbo image-wrapper" width="fit-content" height="fit-content"><img alt="" loading="lazy" width="16" height="16" decoding="async" data-nimg="1" style="color:transparent;object-fit:contain" src="https://www.datocms-assets.com/96965/1728060872-status.svg"/></div></div><div class="sc-ace17a57-0 guuHrd"><span font-weight="medium" display="flex" tabindex="-1" class="sc-b323b31-0 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0ms;color:#9c27b0;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#ffffff;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-es23wo:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(156, 39, 176, 0.04);}@media (hover: none){.css-es23wo:hover{background-color:transparent;}}.css-es23wo.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-es23wo::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#9c27b0;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#ffffff;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-1vy4m6x::-moz-focus-inner{border-style:none;}.css-1vy4m6x.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-1vy4m6x{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-1vy4m6x:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(156, 39, 176, 0.04);}@media (hover: none){.css-1vy4m6x:hover{background-color:transparent;}}.css-1vy4m6x.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-1vy4m6x::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-1vy4m6x:hover{color:#79AFFA;background-color:transparent;}.css-1vy4m6x:focus-visible{color:#ffffff;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-1vy4m6x.Mui-disabled{color:#ffffff;opacity:0.2;}</style><a class="MuiButtonBase-root MuiButton-root MuiButton-text MuiButton-textSecondary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorSecondary MuiButton-root MuiButton-text MuiButton-textSecondary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorSecondary sc-d74559df-0 cIekQB sc-84b76e46-0 sc-f5e67a3c-0 jroYld css-1vy4m6x" tabindex="0" type="button" href="https://console.deepgram.com/" target="_self" id="108492178" __typename="ComponentCallToActionRecord"><span class="sc-b323b31-0 btXZGI button-label" display="inline-flex"><span>Log In</span></span></a><style data-emotion="css 134mfhg">.css-134mfhg{font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 16px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;box-shadow:0px 3px 1px -2px rgba(0,0,0,0.2),0px 2px 2px 0px rgba(0,0,0,0.14),0px 1px 5px 0px rgba(0,0,0,0.12);min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;background:#0B0B0C;color:#ffffff;border:1px solid #ffffff;}.css-134mfhg:hover{-webkit-text-decoration:none;text-decoration:none;box-shadow:0px 2px 4px -1px rgba(0,0,0,0.2),0px 4px 5px 0px rgba(0,0,0,0.14),0px 1px 10px 0px rgba(0,0,0,0.12);}.css-134mfhg:active{box-shadow:0px 5px 5px -3px rgba(0,0,0,0.2),0px 8px 10px 1px rgba(0,0,0,0.14),0px 3px 14px 2px rgba(0,0,0,0.12);}.css-134mfhg.Mui-focusVisible{box-shadow:0px 3px 5px -1px rgba(0,0,0,0.2),0px 6px 10px 0px rgba(0,0,0,0.14),0px 1px 18px 0px 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16px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;box-shadow:0px 3px 1px -2px rgba(0,0,0,0.2),0px 2px 2px 0px rgba(0,0,0,0.14),0px 1px 5px 0px rgba(0,0,0,0.12);min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;background:#0B0B0C;color:#ffffff;border:1px solid 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sc-84b76e46-0 etnILU sc-f5e67a3c-0 jroYeL css-aaf570" tabindex="0" type="button" id="T-CCS94ZQ2CRFyuYD-Kv-Q" __typename="ComponentCallToActionRecord" href="/contact-us"><span class="sc-b323b31-0 fcPowg button-label" display="inline-flex"><span>Get a Demo</span></span></a><style data-emotion="css 40xoaf">.css-40xoaf{font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 16px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:rgba(0, 0, 0, 0.87);background-color:#00E062;box-shadow:0px 3px 1px 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data-emotion="css ubnyan">.css-ubnyan{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:center;-ms-flex-pack:center;-webkit-justify-content:center;justify-content:center;position:relative;box-sizing:border-box;-webkit-tap-highlight-color:transparent;background-color:transparent;outline:0;border:0;margin:0;border-radius:0;padding:0;cursor:pointer;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;vertical-align:middle;-moz-appearance:none;-webkit-appearance:none;-webkit-text-decoration:none;text-decoration:none;color:inherit;font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 16px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:rgba(0, 0, 0, 0.87);background-color:#00E062;box-shadow:0px 3px 1px -2px rgba(0,0,0,0.2),0px 2px 2px 0px rgba(0,0,0,0.14),0px 1px 5px 0px rgba(0,0,0,0.12);min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;background-color:#ffffff;color:#0B0B0C;border:1px solid #ffffff;}.css-ubnyan::-moz-focus-inner{border-style:none;}.css-ubnyan.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ubnyan{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ubnyan:hover{-webkit-text-decoration:none;text-decoration:none;background-color:#00BB49;box-shadow:0px 2px 4px -1px rgba(0,0,0,0.2),0px 4px 5px 0px rgba(0,0,0,0.14),0px 1px 10px 0px rgba(0,0,0,0.12);}@media (hover: none){.css-ubnyan:hover{background-color:#00E062;}}.css-ubnyan:active{box-shadow:0px 5px 5px -3px rgba(0,0,0,0.2),0px 8px 10px 1px rgba(0,0,0,0.14),0px 3px 14px 2px rgba(0,0,0,0.12);}.css-ubnyan.Mui-focusVisible{box-shadow:0px 3px 5px -1px rgba(0,0,0,0.2),0px 6px 10px 0px rgba(0,0,0,0.14),0px 1px 18px 0px rgba(0,0,0,0.12);}.css-ubnyan.Mui-disabled{color:rgba(0, 0, 0, 0.26);box-shadow:none;background-color:rgba(0, 0, 0, 0.12);}.css-ubnyan::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ubnyan::before{background:linear-gradient(to right, #008fc1, #00f099, #008fc1, #00f099);-webkit-background-size:300% 100%;background-size:300% 100%;}.css-ubnyan:hover{color:#0B0B0C;box-shadow:0px 1px 2px rgba(38, 44, 52, 0.05);background:#ffffff;}.css-ubnyan:hover::before{opacity:1;-webkit-background-position:100% 0;background-position:100% 0;}.css-ubnyan:focus{background:#ffffff;box-shadow:0px 1px 2px rgba(16, 24, 40, 0.05),0px 0px 0px 2px #687EF7;border-color:#ffffff;}.css-ubnyan.Mui-disabled{background:#2C2C33;color:#A9A9AD;}</style><a class="MuiButtonBase-root MuiButton-root MuiButton-contained MuiButton-containedPrimary MuiButton-sizeMedium MuiButton-containedSizeMedium MuiButton-colorPrimary MuiButton-root MuiButton-contained MuiButton-containedPrimary MuiButton-sizeMedium MuiButton-containedSizeMedium MuiButton-colorPrimary sc-d74559df-0 cIekQB sc-84b76e46-0 etnILU sc-f5e67a3c-0 jroYeL css-ubnyan" tabindex="0" type="button" href="https://console.deepgram.com/signup" target="_self" id="108492199" __typename="ComponentCallToActionRecord"><span class="sc-b323b31-0 btXZGI button-label" display="inline-flex"><span>Sign Up</span></span></a></div></ul></div></div></div><div display="none" id="nav-overlay" height="0" class="sc-ace17a57-0 jUgQHG"></div></div></nav></div></header><section id="" width="100%" class="sc-ace17a57-0 sc-b22001da-2 iLVWKa eAcnIZ"><div width="100%" class="sc-6293d692-0 chAbBM"><div class="sc-ace17a57-0 doHfou"><a rel="" target="" href="/ai-glossary" class="sc-e69ac761-0 fobbYG"><h2 font-size="displayLg" font-family="primaryFont" class="sc-4555ca6a-0 htUWGk">AI Glossary</h2></a></div></div></section><section id="" width="100%" class="sc-ace17a57-0 sc-b22001da-2 hMGZHr dJJSTR"><div width="100%" class="sc-6293d692-0 chAbBM"><div height="100%" width="100%" class="sc-6293d692-0 gKLLRj"><div height="100%" width="100%" class="sc-662dedcb-0 qCkfD"><div class="sc-6293d692-0 csGpzP"><div class="sc-ace17a57-0 hhtFqm glossary-content-wrapper"><div class="sc-ace17a57-0 btkfVN"><div class="sc-ace17a57-0 sc-a48d0877-0 dJCIVv zIKHU"><h1 font-size="displaySm" letter-spacing="neg2" font-weight="semiBold" font-family="primaryFont" class="sc-b323b31-0 JYZsj">Double Descent</h1><div class="sc-ace17a57-0 fJkbQy"><p font-family="bodyFont" class="sc-5159831f-0 GBftN">This article aims to demystify the concept of double descent in deep learning, providing you with a comprehensive understanding of its implications for model selection and training strategies.</p></div></div></div><div class="sc-ace17a57-0 sc-4e888a2-0 hfDdWp cifBqP"><p class="sc-5159831f-0">Have you ever been intrigued by the way <a href="https://deepgram.com/ai-glossary/deep-learning">deep learning</a> models defy conventional wisdom, especially when it comes to model complexity and overfitting? It’s a common challenge for many in the field: the delicate balancing act of increasing model complexity to improve performance, without inadvertently stepping into the realm of overfitting. Recent research, such as the groundbreaking study from arXiv, has brought to light a phenomenon that challenges these traditional beliefs: the concept of double descent. This revelation not only surprises but also reshapes our understanding of overparameterization and generalization error in deep learning.</p><p class="sc-5159831f-0">This article aims to demystify the concept of double descent in deep learning, providing you with a comprehensive understanding of its implications for model selection and training strategies. By exploring key terms such as overparameterization, generalization error, and the bias-variance tradeoff, we'll delve into how double descent defies the long-held principle of the bias-variance tradeoff. The significance of this phenomenon in explaining the unprecedented success of deep neural networks cannot be overstated. As we set the stage for a deeper dive into the specifics of double descent, ask yourself: how might this insight change the way you approach model complexity in your deep learning projects?</p><h2 id="introduction-to-double-descent" class="sc-4555ca6a-0 sc-42818e5a-3 kIEulY ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Introduction to Double Descent</span></h2><p class="sc-5159831f-0">The concept of double descent in deep learning offers an intriguing twist to the narrative of overfitting and model complexity. At its core, double descent describes a phenomenon where increasing the complexity of a model beyond a certain point—contrary to leading to overfitting—actually improves its performance on test data. This challenges the traditional view encapsulated by the bias-variance tradeoff, which suggests that after a certain point, increasing a model's complexity leads to a decrease in its ability to generalize to unseen data. Let's unpack some key aspects of this phenomenon:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Overparameterization: This refers to situations where the number of parameters in a model far exceeds the number of training data points. Surprisingly, models in the highly overparameterized regime can achieve better test error rates, a finding supported by a study on arXiv.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Generalization Error: The discrepancy between a model's performance on training data and unseen data. The double descent curve reveals that generalization error decreases, increases, and then decreases again as model complexity grows, painting a complex picture of how deep learning models learn.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Bias-Variance Tradeoff: Historically, the bias-variance tradeoff has been a guiding principle in understanding the relationship between model complexity and generalization error. However, the existence of double descent suggests that this tradeoff does not fully capture the dynamics at play in deep learning models.</p></li></li></ul><p class="sc-5159831f-0">The discovery of double descent challenges us to rethink model selection and training strategies in deep learning. It underscores the importance of exploring models in the highly overparameterized regime and offers a fresh perspective on why deep neural networks have achieved remarkable success across a range of applications. As we proceed, we delve deeper into the mechanics of double descent in the context of deep learning models, exploring its implications through examples from recent studies and discussing its impact on training strategies.</p><h2 id="double-descent-in-deep-learning-models" class="sc-4555ca6a-0 sc-42818e5a-3 kIEulY ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Double Descent in Deep Learning Models</span></h2><p class="sc-5159831f-0">The journey through the landscape of deep learning models reveals an intriguing phenomenon known as double descent. This phenomenon, observed in the behavior of two-layer neural networks among others, provides a novel perspective on model complexity and its impact on test error rates. Let's explore the mechanics and implications of this phenomenon in detail.</p><h3 id="the-mechanics-of-double-descent" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">The Mechanics of Double Descent</span></h3><p class="sc-5159831f-0">Double descent occurs in a three-phase process:</p><ol class="sc-ace17a57-0 sc-42818e5a-2 QuIBn eBBHJ"><li><p class="sc-5159831f-0">Underfitting Phase: As the complexity of a deep learning model begins to increase, the test error decreases. This phase is characterized by models that are not complex enough to capture the underlying patterns in the data, leading to high bias.</p></li><li><p class="sc-5159831f-0">Overfitting Phase: Continuing to add complexity to the model leads to an increase in test error. During this phase, models are too complex relative to the amount of training data, capturing noise as if it were signal, which results in high variance.</p></li><li><p class="sc-5159831f-0">Second Descent: Remarkably, as model complexity grows even further, entering the highly overparameterized regime, the test error begins to decrease once again. This counterintuitive phase defies traditional expectations about overfitting.</p></li></ol><h3 id="examples-from-recent-studies" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Examples from Recent Studies</span></h3><p class="sc-5159831f-0">Recent research has illuminated the occurrence of double descent across various deep learning architectures:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Convolutional Neural Networks (CNNs), Residual Networks (ResNets), and Transformers have all demonstrated this phenomenon, as highlighted by OpenAI's research on deep double descent. These architectures initially exhibit decreased test error, encounter a peak of increased error, and then surprisingly show a decline in error as model complexity continues to grow.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">The role of model parameters and the ratio of parameters to data points is crucial in triggering double descent. Models with a high parameter-to-data point ratio enter the overparameterized regime, where the second descent becomes observable.</p></li></li></ul><h3 id="the-implications-of-double-descent" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">The Implications of Double Descent</span></h3><p class="sc-5159831f-0">Understanding double descent has significant implications for the design and training of deep learning models:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">It challenges the conventional wisdom that there is a straightforward trade-off between bias and variance as model complexity increases.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">The phenomenon suggests that in certain cases, increasing model size could lead to better generalization, even in the absence of additional data.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">This insight informs the choice of model size, encouraging practitioners to consider highly overparameterized models as viable and potentially optimal choices for certain tasks.</p></li></li></ul><h3 id="epochwise-double-descent" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Epoch-wise Double Descent</span></h3><p class="sc-5159831f-0">Not limited to model complexity, double descent also manifests across training epochs:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">As discussed in a study on arXiv, epoch-wise double descent occurs at specific noise levels and parameter values. The phenomenon is observed when training for an extended number of epochs, showcasing a similar pattern of test error reduction after an initial increase.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">This suggests that not only the architecture and size of the model but also the duration of training and the presence of noise in the data can influence the occurrence of double descent.</p></li></li></ul><p class="sc-5159831f-0">Double descent offers a nuanced view of the relationship between model complexity and generalization in deep learning. It underscores the importance of exploring a wider range of model architectures and sizes, as well as training durations, to fully leverage the potential of deep neural networks. The phenomenon of double descent, with its surprising second descent in test error, challenges long-held beliefs and opens new avenues for research and application in the field of deep learning.</p><p class="sc-5159831f-0"><div width="100%" class="sc-ace17a57-0 ldWHw component-img-wrapper" id="NpVOtWPlToearVCrOThlKA"><div class="sc-ace17a57-0 sc-5f7d928-0 iLvNR kritbo image-wrapper" width="fit-content" height="fit-content" display="flex"><img alt="" title="" loading="lazy" width="1798" height="1074" decoding="async" data-nimg="1" class="sc-3ec8aa52-0 jTMTOn desktop-image" style="color:transparent;object-fit:contain;background-size:contain;background-position:50% 50%;background-repeat:no-repeat;background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 1798 1074'%3E%3Cfilter id='b' color-interpolation-filters='sRGB'%3E%3CfeGaussianBlur stdDeviation='20'/%3E%3CfeColorMatrix values='1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 100 -1' result='s'/%3E%3CfeFlood x='0' y='0' width='100%25' height='100%25'/%3E%3CfeComposite operator='out' in='s'/%3E%3CfeComposite in2='SourceGraphic'/%3E%3CfeGaussianBlur stdDeviation='20'/%3E%3C/filter%3E%3Cimage width='100%25' height='100%25' x='0' y='0' preserveAspectRatio='none' style='filter: url(%23b);' href='/deepgram.jpg'/%3E%3C/svg%3E")" sizes="(min-width: 992px) 810px, 100vw" srcSet="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736413-screen-shot-2024-06-18-at-11-46-49-am.png&w=640&q=75 640w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736413-screen-shot-2024-06-18-at-11-46-49-am.png&w=750&q=75 750w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736413-screen-shot-2024-06-18-at-11-46-49-am.png&w=828&q=75 828w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736413-screen-shot-2024-06-18-at-11-46-49-am.png&w=1080&q=75 1080w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736413-screen-shot-2024-06-18-at-11-46-49-am.png&w=1200&q=75 1200w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736413-screen-shot-2024-06-18-at-11-46-49-am.png&w=1920&q=75 1920w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736413-screen-shot-2024-06-18-at-11-46-49-am.png&w=2048&q=75 2048w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736413-screen-shot-2024-06-18-at-11-46-49-am.png&w=3840&q=75 3840w" src="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736413-screen-shot-2024-06-18-at-11-46-49-am.png&w=3840&q=75"/></div><div font-size="textSm" font-style="italic" class="sc-6293d692-0 jgEMAk"></div></div></p><h2 id="the-impact-of-double-descent-on-training" class="sc-4555ca6a-0 sc-42818e5a-3 kIEulY ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">The Impact of Double Descent on Training</span></h2><p class="sc-5159831f-0">The phenomenon of double descent significantly influences training strategies and outcomes in deep learning. As we navigate this complex landscape, understanding its impact enables us to refine our approaches to model selection, training duration, and data management.</p><h3 id="navigating-the-double-descent-curve" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Navigating the Double Descent Curve</span></h3><p class="sc-5159831f-0">Strategising around the double descent curve involves several key considerations:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Model Size Selection: The perplexing nature of double descent necessitates a departure from traditional model selection strategies. Instead of avoiding overparameterization, embracing larger models may lead to better generalization in the regime beyond the double descent peak. This counterintuitive approach requires careful experimentation to identify the optimal model size that leverages the second descent for improved test error rates.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Training Duration: The occurrence of epoch-wise double descent suggests that the duration of training also plays a critical role. Extending training beyond the point where overfitting typically occurs can unexpectedly reduce test errors. However, this demands precise control and monitoring to avoid excessive training that may not yield further improvements.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Data Management: In the face of double descent, the importance of data quality and quantity becomes even more pronounced. Highly overparameterized models have an insatiable appetite for data, making the acquisition of larger, high-quality datasets a priority. Simultaneously, data preprocessing and augmentation techniques gain importance to maximize the utility of available data.</p></li></li></ul><h3 id="implications-for-early-stopping-and-regularization" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Implications for Early Stopping and Regularization</span></h3><p class="sc-5159831f-0">Double descent reshapes the landscape of model training techniques:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Early Stopping: The traditional practice of early stopping to prevent overfitting must be revisited. Given the potential benefits of navigating past the overfitting peak into the second descent, determining the optimal stopping point becomes more nuanced. Experimentation and validation against a holdout dataset are crucial to identify when further training ceases to yield benefits.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Regularization Techniques: While regularization remains a cornerstone of combating overfitting, its role is nuanced in the context of double descent. Techniques such as dropout or weight decay must be applied judiciously, balancing the need to prevent overfitting against the possibility of hindering the model's journey into the beneficial overparameterized regime.</p></li></li></ul><h3 id="leveraging-insights-from-the-machine-learning-community" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Leveraging Insights from the Machine Learning Community</span></h3><p class="sc-5159831f-0">The <a href="https://deepgram.com/ai-glossary/machine-learning">machine learning</a> community provides valuable insights into managing double descent:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Luca Massaron's Advice: In his exploration of deep learning for tabular data, Luca Massaron emphasizes the challenges posed by sparse data and the lack of best practice architectures. His recommendation to use regularization techniques like L1/L2 and dropout, alongside feature engineering, offers a roadmap for navigating double descent in practical applications.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Architectural Considerations: The choice of neural architecture plays a pivotal role in mitigating the impacts of double descent. Specific architectures, informed by the latest research and community insights, can be more resilient to the pitfalls of overparameterization. Experimentation with different configurations and adherence to best practices are key to harnessing the benefits of double descent.</p></li></li></ul><h3 id="identifying-the-optimal-stopping-point" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Identifying the Optimal Stopping Point</span></h3><p class="sc-5159831f-0">One of the most daunting challenges in the era of double descent is pinpointing the optimal moment to halt model training. This decision requires a delicate balance, aiming to maximize generalization without succumbing to the detrimental effects of overfitting. Rigorous validation, coupled with an awareness of the double descent phenomenon, guides this critical decision-making process.</p><p class="sc-5159831f-0">The journey through the double descent phenomenon in deep learning is complex and fraught with counterintuitive insights. However, armed with a deep understanding of its mechanics and implications, practitioners can navigate this landscape more effectively, optimizing their models for superior performance and generalization.</p><p class="sc-5159831f-0"><div width="100%" class="sc-ace17a57-0 ldWHw component-img-wrapper" id="AGJOfobER-azW9kVyt5ZiA"><div class="sc-ace17a57-0 sc-5f7d928-0 iLvNR kritbo image-wrapper" width="fit-content" height="fit-content" display="flex"><img alt="" title="" loading="lazy" width="1796" height="1088" decoding="async" data-nimg="1" class="sc-3ec8aa52-0 jTMTOn desktop-image" style="color:transparent;object-fit:contain;background-size:contain;background-position:50% 50%;background-repeat:no-repeat;background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 1796 1088'%3E%3Cfilter id='b' color-interpolation-filters='sRGB'%3E%3CfeGaussianBlur stdDeviation='20'/%3E%3CfeColorMatrix values='1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 100 -1' result='s'/%3E%3CfeFlood x='0' y='0' width='100%25' height='100%25'/%3E%3CfeComposite operator='out' in='s'/%3E%3CfeComposite in2='SourceGraphic'/%3E%3CfeGaussianBlur stdDeviation='20'/%3E%3C/filter%3E%3Cimage width='100%25' height='100%25' x='0' y='0' preserveAspectRatio='none' style='filter: url(%23b);' href='/deepgram.jpg'/%3E%3C/svg%3E")" sizes="(min-width: 992px) 810px, 100vw" srcSet="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736518-screen-shot-2024-06-18-at-11-48-34-am.png&w=640&q=75 640w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736518-screen-shot-2024-06-18-at-11-48-34-am.png&w=750&q=75 750w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736518-screen-shot-2024-06-18-at-11-48-34-am.png&w=828&q=75 828w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736518-screen-shot-2024-06-18-at-11-48-34-am.png&w=1080&q=75 1080w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736518-screen-shot-2024-06-18-at-11-48-34-am.png&w=1200&q=75 1200w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736518-screen-shot-2024-06-18-at-11-48-34-am.png&w=1920&q=75 1920w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736518-screen-shot-2024-06-18-at-11-48-34-am.png&w=2048&q=75 2048w, /_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736518-screen-shot-2024-06-18-at-11-48-34-am.png&w=3840&q=75 3840w" src="/_next/image?url=https%3A%2F%2Fwww.datocms-assets.com%2F96965%2F1718736518-screen-shot-2024-06-18-at-11-48-34-am.png&w=3840&q=75"/></div><div font-size="textSm" font-style="italic" class="sc-6293d692-0 jgEMAk"></div></div></p><h2 id="identifying-and-interpreting-double-descent" class="sc-4555ca6a-0 sc-42818e5a-3 kIEulY ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Identifying and Interpreting Double Descent</span></h2><p class="sc-5159831f-0">The double descent phenomenon in deep learning, while initially counterintuitive, has profound implications on how we approach model training and complexity. Understanding and identifying this phenomenon is not just an academic exercise but a practical necessity for improving model performance. This section delves into the methodologies for spotting double descent, the tools at our disposal, and real-world implications, providing a comprehensive guide for practitioners.</p><h3 id="methods-for-plotting-and-analyzing-test-error" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Methods for Plotting and Analyzing Test Error</span></h3><p class="sc-5159831f-0">Identifying the double descent curve requires meticulous analysis of test error as a function of model complexity or training epochs. Here's how:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Plotting Test Error vs. Model Complexity: Start by incrementally increasing the model's complexity, plotting the test error at each step. The initial decrease, subsequent increase, and eventual second decrease in test error illustrate the double descent curve. Tools like Matplotlib or Seaborn in Python are instrumental for this visualization.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Analyzing Error over Training Epochs: Similarly, plotting test error as a function of training epochs can reveal an epoch-wise double descent. This requires tracking test errors across training epochs, a task for which deep learning frameworks like TensorFlow or PyTorch are well-suited.</p></li></li></ul><h3 id="tools-and-libraries-for-visualization" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Tools and Libraries for Visualization</span></h3><p class="sc-5159831f-0">Several tools and libraries can aid in visualizing the double descent phenomenon:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Python Libraries: Utilize Matplotlib, Seaborn, or Plotly for creating comprehensive plots that clearly illustrate the double descent curve. These libraries offer flexibility in data visualization, allowing for detailed analysis.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Deep Learning Frameworks: TensorFlow and PyTorch not only facilitate model training but also provide utilities for monitoring training progress, including test errors, which are crucial for identifying double descent.</p></li></li></ul><h3 id="understanding-data-distribution-and-model-assumptions" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Understanding Data Distribution and Model Assumptions</span></h3><p class="sc-5159831f-0">A deep understanding of the underlying data distribution and model assumptions is essential when interpreting double descent:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Data Distribution: Recognize that the double descent phenomenon is influenced by the data's characteristics, including its distribution and noise level. Anomalies in data can significantly impact the model's learning curve and test errors.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Model Assumptions: Each model comes with its set of assumptions about the data it's learning from. When identifying double descent, consider how these assumptions interact with the data's actual characteristics.</p></li></li></ul><h3 id="realworld-applications-and-case-studies" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Real-World Applications and Case Studies</span></h3><p class="sc-5159831f-0">Double descent has been observed and addressed in various real-world applications, offering valuable insights:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Image Classification: In tasks like image classification, researchers have documented the double descent phenomenon across different architectures, including CNNs and ResNets. These case studies provide practical examples of double descent in action, highlighting the significance of model complexity and training strategy adjustments.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0"><a href="https://deepgram.com/ai-glossary/natural-language-processing">Natural Language Processing (NLP)</a>: Similarly, in NLP tasks, models like transformers have exhibited double descent behavior, underscoring the importance of data management and model selection strategies tailored to this phenomenon.</p></li></li></ul><h3 id="mathematical-explanation-for-double-descent" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Mathematical Explanation for Double Descent</span></h3><p class="sc-5159831f-0">A deeper understanding of double descent comes from diving into its mathematical foundations:</p><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Prediction Risk and Overparameterization: The mathematical explanation for double descent, as discussed on naologic.com, delineates how overparameterization—having more parameters in the model than data points—leads to a reduction in prediction risk after an initial increase. This elucidates why larger models can, paradoxically, generalize better in certain regimes.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Bias-Variance Tradeoff Revisited: Double descent offers a new perspective on the bias-variance tradeoff, highlighting scenarios where traditional models of this tradeoff do not apply. Understanding the mathematical underpinnings of double descent provides a theoretical basis for its practical observations.</p></li></li></ul><p class="sc-5159831f-0">Identifying and interpreting double descent requires a blend of visualization techniques, a solid grasp of the underlying data and model dynamics, and an appreciation of its mathematical basis. By leveraging these insights, practitioners can better navigate the complexities of model training in the era of deep learning, optimizing their approaches for improved performance and generalization.</p><h2 id="double-descent-and-the-biasvariance-tradeoff" class="sc-4555ca6a-0 sc-42818e5a-3 kIEulY ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Double Descent and the Bias-Variance Tradeoff</span></h2><p class="sc-5159831f-0">The bias-variance tradeoff has long stood as a cornerstone principle in the realm of machine learning, guiding practitioners in their quest for the optimal balance between model simplicity and complexity. However, the discovery of the double descent phenomenon has cast this traditional model into a new light, suggesting there are realms of model behavior previously unaccounted for.</p><h3 id="a-new-perspective-on-model-error-decomposition" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">A New Perspective on Model Error Decomposition</span></h3><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Challenging Traditional Models: Double descent reveals that increasing model complexity beyond a certain point can actually lead to improved test error rates, challenging the traditional view where increasing complexity indefinitely leads to overfitting.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Evidence of Model-Wise and Epoch-Wise Regimes: Unlike the classical bias-variance tradeoff, which suggests a monotonous relationship between model complexity and error, double descent indicates the existence of distinct phases or regimes in the training process. This includes both model-wise regimes, where increasing the number of parameters can lead to better performance, and epoch-wise regimes, where training duration also impacts error rates in non-linear ways.</p></li></li></ul><h3 id="theoretical-implications-for-deep-learning-models" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Theoretical Implications for Deep Learning Models</span></h3><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Beyond Overfitting: The phenomenon provides concrete evidence that the capacity of deep learning models to generalize cannot solely be explained through the lens of overfitting. This has profound implications for how we understand model training and generalization.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Mikhail Belkin’s Contribution: Mikhail Belkin's work, referenced in the Communications of the ACM, has been pivotal in shedding light on the double descent phenomenon. His research underscores the complexity of learning dynamics in highly overparameterized models and the need to rethink generalization in this context.</p></li></li></ul><h3 id="double-descent-challenge-or-complement-to-biasvariance" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Double Descent: Challenge or Complement to Bias-Variance?</span></h3><ul class="sc-ace17a57-0 sc-42818e5a-1 dslPBO dZzOHq"><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">A Complementary Perspective: While double descent appears to challenge the traditional bias-variance tradeoff, it might also be seen as a complement, expanding our understanding of model behavior in highly parameterized regimes. It suggests that the bias-variance tradeoff is not obsolete but rather incomplete, lacking in its accounting for modern deep learning architectures.</p></li></li><li class="sc-ace17a57-0 sc-42818e5a-0 PRHwk hegRkn"><li><p class="sc-5159831f-0">Implications for Model Selection: The acknowledgment of double descent necessitates a more nuanced approach to model selection and training strategy. It implies that the path to optimal model performance is not simply a matter of minimizing complexity but may involve embracing and navigating through phases of increased complexity.</p></li></li></ul><h3 id="future-research-directions" class="sc-4555ca6a-0 sc-42818e5a-3 cGaypB ipqlKg"><span font-weight="bold" class="sc-b323b31-0 caUwZV">Future Research Directions</span></h3><p class="sc-5159831f-0">The exploration of double descent opens up new avenues for research, particularly in the study of deep learning models' generalization capabilities. The existence of model-wise and epoch-wise double descent regimes invites further investigation into the underlying mathematical principles and practical strategies for model training. This could lead to the development of new methodologies for model selection, training protocols, and even architectural innovations designed to harness the potential of the double descent curve.</p><p class="sc-5159831f-0">Understanding double descent not only enriches our conceptual toolkit but also equips practitioners with a more sophisticated framework for navigating the complexities of machine learning. As research continues to unravel the intricacies of this phenomenon, the potential for groundbreaking insights into the behavior of complex learning systems remains immense, promising to reshape our approaches to model training and generalization in profound ways.</p><p class="sc-5159831f-0"><div width="100%" class="sc-ace17a57-0 ldWHw component-img-wrapper" id="OcUPVLYOTdiOH90vXDPFbA"><div class="sc-ace17a57-0 sc-5f7d928-0 iLvNR kritbo image-wrapper" width="fit-content" height="fit-content" display="flex"><img alt="" title="" loading="lazy" width="1512" height="788" decoding="async" data-nimg="1" class="sc-3ec8aa52-0 jTMTOn desktop-image" style="color:transparent;object-fit:contain;background-size:contain;background-position:50% 50%;background-repeat:no-repeat;background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 1512 788'%3E%3Cfilter id='b' color-interpolation-filters='sRGB'%3E%3CfeGaussianBlur 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kmKRMV">Multi-task Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/naive-bayes-classifier" class="sc-e69ac761-0 kmKRMV">Naive Bayes Classifier</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-neuron" class="sc-e69ac761-0 kmKRMV">Machine Learning Neuron</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pooling-machine-learning" class="sc-e69ac761-0 kmKRMV">Pooling (Machine Learning)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/principal-component-analysis" class="sc-e69ac761-0 kmKRMV">Principal Component Analysis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-preprocessing" class="sc-e69ac761-0 kmKRMV">Machine Learning Preprocessing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/rectified-linear-unit-relu" class="sc-e69ac761-0 kmKRMV">Rectified Linear Unit (ReLU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/reproducibility-machine-learning" class="sc-e69ac761-0 kmKRMV">Reproducibility in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/restricted-boltzmann-machines" class="sc-e69ac761-0 kmKRMV">Restricted Boltzmann Machines</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semi-supervised-learning" class="sc-e69ac761-0 kmKRMV">Semi-Supervised Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/supervised-learning" class="sc-e69ac761-0 kmKRMV">Supervised Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/support-vector-machines-svm" class="sc-e69ac761-0 kmKRMV">Support Vector Machines (SVM)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/topic-modeling" class="sc-e69ac761-0 kmKRMV">Topic Modeling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/uncertainty-machine-learning" class="sc-e69ac761-0 kmKRMV">Uncertainty in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/vanishing-and-exploding-gradients" class="sc-e69ac761-0 kmKRMV">Vanishing and Exploding Gradients</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-interpretability" class="sc-e69ac761-0 kmKRMV">AI Interpretability</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-labeling" class="sc-e69ac761-0 kmKRMV">Data Labeling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/inference-engine" class="sc-e69ac761-0 kmKRMV">Inference Engine</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/probabilistic-models-in-machine-learning" class="sc-e69ac761-0 kmKRMV">Probabilistic Models in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/f1-score-machine-learning" class="sc-e69ac761-0 kmKRMV">F1 Score in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/expectation-maximization" class="sc-e69ac761-0 kmKRMV">Expectation Maximization</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/beam-search-algorithm" class="sc-e69ac761-0 kmKRMV">Beam Search Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/embedding-layer" class="sc-e69ac761-0 kmKRMV">Embedding Layer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/differential-privacy" class="sc-e69ac761-0 kmKRMV">Differential Privacy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-poisoning" class="sc-e69ac761-0 kmKRMV">Data Poisoning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/causal-inference" class="sc-e69ac761-0 kmKRMV">Causal Inference</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/capsule-neural-network" class="sc-e69ac761-0 kmKRMV">Capsule Neural Network</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/attention-mechanisms" class="sc-e69ac761-0 kmKRMV">Attention Mechanisms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/domain-adaptation" class="sc-e69ac761-0 kmKRMV">Domain Adaptation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/evolutionary-algorithms" class="sc-e69ac761-0 kmKRMV">Evolutionary Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/contrastive-learning" class="sc-e69ac761-0 kmKRMV">Contrastive Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/explainable-ai" class="sc-e69ac761-0 kmKRMV">Explainable AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/affective-ai" class="sc-e69ac761-0 kmKRMV">Affective AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semantic-networks" class="sc-e69ac761-0 kmKRMV">Semantic Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-augmentation" class="sc-e69ac761-0 kmKRMV">Data Augmentation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/convolutional-neural-networks" class="sc-e69ac761-0 kmKRMV">Convolutional Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-computing" class="sc-e69ac761-0 kmKRMV">Cognitive Computing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/end-to-end-learning" class="sc-e69ac761-0 kmKRMV">End-to-end Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/prompt-tuning" class="sc-e69ac761-0 kmKRMV">Prompt Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/double-descent" class="sc-e69ac761-0 iUnKGS">Double Descent</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/model-drift" class="sc-e69ac761-0 kmKRMV">Model Drift</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-radiance-fields" class="sc-e69ac761-0 kmKRMV">Neural Radiance Fields</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/regularization" class="sc-e69ac761-0 kmKRMV">Regularization</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-querying" class="sc-e69ac761-0 kmKRMV">Natural Language Querying (NLQ)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/foundation-models" class="sc-e69ac761-0 kmKRMV">Foundation Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/forward-propagation" class="sc-e69ac761-0 kmKRMV">Forward Propagation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/f2-score" class="sc-e69ac761-0 kmKRMV">F2 Score</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-ethics" class="sc-e69ac761-0 kmKRMV">AI Ethics</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/transfer-learning" class="sc-e69ac761-0 kmKRMV">Transfer Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-alignment" class="sc-e69ac761-0 kmKRMV">AI Alignment</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/whisper-v3" class="sc-e69ac761-0 kmKRMV">Whisper v3</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/whisper-v2" class="sc-e69ac761-0 kmKRMV">Whisper v2</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semi-structured-data" class="sc-e69ac761-0 kmKRMV">Semi-structured data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-hallucinations" class="sc-e69ac761-0 kmKRMV">AI Hallucinations</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/emergent-behavior" class="sc-e69ac761-0 kmKRMV">Emergent Behavior</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/matplotlib" class="sc-e69ac761-0 kmKRMV">Matplotlib</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/numpy" class="sc-e69ac761-0 kmKRMV">NumPy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/scikit-learn" class="sc-e69ac761-0 kmKRMV">Scikit-learn</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/scipy" class="sc-e69ac761-0 kmKRMV">SciPy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/keras" class="sc-e69ac761-0 kmKRMV">Keras</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/tensorflow" class="sc-e69ac761-0 kmKRMV">TensorFlow</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/seaborn-python-package" class="sc-e69ac761-0 kmKRMV">Seaborn Python Package</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pytorch" class="sc-e69ac761-0 kmKRMV">PyTorch</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-toolkit-nltk" class="sc-e69ac761-0 kmKRMV">Natural Language Toolkit (NLTK)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pandas" class="sc-e69ac761-0 kmKRMV">Pandas</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ego-4d" class="sc-e69ac761-0 kmKRMV">Ego 4D</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/the-pile" class="sc-e69ac761-0 kmKRMV">The Pile</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/common-crawl-datasets" class="sc-e69ac761-0 kmKRMV">Common Crawl Datasets</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/squad" class="sc-e69ac761-0 kmKRMV">SQuAD</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/intelligent-document-processing" class="sc-e69ac761-0 kmKRMV">Intelligent Document Processing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hyperparameter-tuning" class="sc-e69ac761-0 kmKRMV">Hyperparameter Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/Markov-decision-process" class="sc-e69ac761-0 kmKRMV">Markov Decision Process</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/graph-neural-networks" class="sc-e69ac761-0 kmKRMV">Graph Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-architecture-search" class="sc-e69ac761-0 kmKRMV">Neural Architecture Search</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ablation" class="sc-e69ac761-0 kmKRMV">Ablation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/knowledge-distillation" class="sc-e69ac761-0 kmKRMV">Knowledge Distillation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/model-interpretability" class="sc-e69ac761-0 kmKRMV">Model Interpretability</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/out-of-distribution-detection" class="sc-e69ac761-0 kmKRMV">Out-of-Distribution Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/recurrent-neural-networks" class="sc-e69ac761-0 kmKRMV">Recurrent Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/active-learning" class="sc-e69ac761-0 kmKRMV">Active Learning (Machine Learning)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/imbalanced-data" class="sc-e69ac761-0 kmKRMV">Imbalanced Data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/loss-function" class="sc-e69ac761-0 kmKRMV">Loss Function</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/unsupervised-learning" class="sc-e69ac761-0 kmKRMV">Unsupervised Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-and-big-data" class="sc-e69ac761-0 kmKRMV">AI and Big Data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/adagrad" class="sc-e69ac761-0 kmKRMV">AdaGrad</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/clustering-algorithms" class="sc-e69ac761-0 kmKRMV">Clustering Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/parametric-neural-networks%C2%A0" class="sc-e69ac761-0 kmKRMV">Parametric Neural Networks </a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/acoustic-models" class="sc-e69ac761-0 kmKRMV">Acoustic Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/articulatory-synthesis" class="sc-e69ac761-0 kmKRMV">Articulatory Synthesis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/concatenative-synthesis" class="sc-e69ac761-0 kmKRMV">Concatenative Synthesis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/grapheme-to-phoneme-conversion-g2p" class="sc-e69ac761-0 kmKRMV">Grapheme-to-Phoneme Conversion (G2P)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/homograph-disambiguation" class="sc-e69ac761-0 kmKRMV">Homograph Disambiguation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-text-to-speech-ntts" class="sc-e69ac761-0 kmKRMV">Neural Text-to-Speech (NTTS)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/voice-cloning" class="sc-e69ac761-0 kmKRMV">Voice Cloning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/autoregressive-model" class="sc-e69ac761-0 kmKRMV">Autoregressive Model</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/candidate-sampling" class="sc-e69ac761-0 kmKRMV">Candidate Sampling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-algorithmic-trading" class="sc-e69ac761-0 kmKRMV">Machine Learning in Algorithmic Trading</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-creativity" class="sc-e69ac761-0 kmKRMV">Computational Creativity</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/context-aware-computing" class="sc-e69ac761-0 kmKRMV">Context-Aware Computing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-emotion-recognition" class="sc-e69ac761-0 kmKRMV">AI Emotion Recognition</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/knowledge-representation-and-reasoning" class="sc-e69ac761-0 kmKRMV">Knowledge Representation and Reasoning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/metacognitive-learning-models" class="sc-e69ac761-0 kmKRMV">Metacognitive Learning Models </a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/synthetic-data-for-ai-training" class="sc-e69ac761-0 kmKRMV">Synthetic Data for AI Training</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-speech-enhancement" class="sc-e69ac761-0 kmKRMV">AI Speech Enhancement</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/counterfactual-explanations-in-ai" class="sc-e69ac761-0 kmKRMV">Counterfactual Explanations in AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/eco-friendly-ai" class="sc-e69ac761-0 kmKRMV">Eco-friendly AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feature-store-for-machine-learning" class="sc-e69ac761-0 kmKRMV">Feature Store for Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/generative-teaching-networks" class="sc-e69ac761-0 kmKRMV">Generative Teaching Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/human-centered-ai" class="sc-e69ac761-0 kmKRMV">Human-centered AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/metaheuristic-algorithms" class="sc-e69ac761-0 kmKRMV">Metaheuristic Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/statistical-relational-learning" class="sc-e69ac761-0 kmKRMV">Statistical Relational Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-architectures" class="sc-e69ac761-0 kmKRMV">Cognitive Architectures</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-phenotyping" class="sc-e69ac761-0 kmKRMV">Computational Phenotyping</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/continuous-learning-systems" class="sc-e69ac761-0 kmKRMV">Continuous Learning Systems</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/deepfake-detection" class="sc-e69ac761-0 kmKRMV">Deepfake Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/one-shot-learning" class="sc-e69ac761-0 kmKRMV">One-Shot Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/quantum-machine-learning-algorithms" class="sc-e69ac761-0 kmKRMV">Quantum Machine Learning Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/self-healing-ai" class="sc-e69ac761-0 kmKRMV">Self-healing AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semantic-search-algorithms" class="sc-e69ac761-0 kmKRMV">Semantic Search Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/artificial-super-intelligence" class="sc-e69ac761-0 kmKRMV">Artificial Super Intelligence</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-guardrails" class="sc-e69ac761-0 kmKRMV">AI Guardrails</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/limited-memory-ai" class="sc-e69ac761-0 kmKRMV">Limited Memory AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/chatbots" class="sc-e69ac761-0 kmKRMV">Chatbots</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/diffusion" class="sc-e69ac761-0 kmKRMV">Diffusion</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hidden-layer" class="sc-e69ac761-0 kmKRMV">Hidden Layer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/instruction-tuning" class="sc-e69ac761-0 kmKRMV">Instruction Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/objective-function" class="sc-e69ac761-0 kmKRMV">Objective Function</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pretraining" class="sc-e69ac761-0 kmKRMV">Pretraining</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/symbolic-ai" class="sc-e69ac761-0 kmKRMV">Symbolic AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/auto-classification" 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css ak4akz">.css-ak4akz{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:center;-ms-flex-pack:center;-webkit-justify-content:center;justify-content:center;position:relative;box-sizing:border-box;-webkit-tap-highlight-color:transparent;background-color:transparent;outline:0;border:0;margin:0;border-radius:0;padding:0;cursor:pointer;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;vertical-align:middle;-moz-appearance:none;-webkit-appearance:none;-webkit-text-decoration:none;text-decoration:none;color:inherit;font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root MuiButton-root MuiButton-text MuiButton-textPrimary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorPrimary MuiButton-root MuiButton-text MuiButton-textPrimary MuiButton-sizeMedium MuiButton-textSizeMedium MuiButton-colorPrimary sc-d74559df-0 iotBFW css-ak4akz" tabindex="0" type="button" href="" target="_self"><span class="sc-b323b31-0 btXZGI button-label" display="inline-flex">I</span></button></li><li class="sc-ace17a57-0 goWpow"><style data-emotion="css q0kznr">.css-q0kznr{font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css ak4akz">.css-ak4akz{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:center;-ms-flex-pack:center;-webkit-justify-content:center;justify-content:center;position:relative;box-sizing:border-box;-webkit-tap-highlight-color:transparent;background-color:transparent;outline:0;border:0;margin:0;border-radius:0;padding:0;cursor:pointer;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;vertical-align:middle;-moz-appearance:none;-webkit-appearance:none;-webkit-text-decoration:none;text-decoration:none;color:inherit;font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css ak4akz">.css-ak4akz{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:center;-ms-flex-pack:center;-webkit-justify-content:center;justify-content:center;position:relative;box-sizing:border-box;-webkit-tap-highlight-color:transparent;background-color:transparent;outline:0;border:0;margin:0;border-radius:0;padding:0;cursor:pointer;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;vertical-align:middle;-moz-appearance:none;-webkit-appearance:none;-webkit-text-decoration:none;text-decoration:none;color:inherit;font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media print{.css-ak4akz{-webkit-print-color-adjust:exact;color-adjust:exact;}}.css-ak4akz:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-ak4akz:hover{background-color:transparent;}}.css-ak4akz.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-ak4akz::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-ak4akz:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-ak4akz:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-ak4akz.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><button class="MuiButtonBase-root 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;border-radius:4px;box-sizing:content-box;padding:1px;}.css-q0kznr:hover{color:#ffffff;-webkit-text-decoration:underline;text-decoration:underline;background-color:transparent;}.css-q0kznr:focus-visible{color:#ffffff;-webkit-text-decoration:none;text-decoration:none;border-radius:4px;outline:2px solid #687EF7;outline-offset:3px;}.css-q0kznr.Mui-disabled{color:#96A2FF;opacity:0.5;}</style><style data-emotion="css ak4akz">.css-ak4akz{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-box-pack:center;-ms-flex-pack:center;-webkit-justify-content:center;justify-content:center;position:relative;box-sizing:border-box;-webkit-tap-highlight-color:transparent;background-color:transparent;outline:0;border:0;margin:0;border-radius:0;padding:0;cursor:pointer;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;vertical-align:middle;-moz-appearance:none;-webkit-appearance:none;-webkit-text-decoration:none;text-decoration:none;color:inherit;font-family:var(--font-inter, sans-serif);font-size:0.875rem;line-height:1.75rem;font-weight:700;text-transform:uppercase;min-width:64px;padding:6px 8px;border-radius:4px;-webkit-transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-q0kznr:hover{-webkit-text-decoration:none;text-decoration:none;background-color:rgba(0, 224, 98, 0.04);}@media (hover: none){.css-q0kznr:hover{background-color:transparent;}}.css-q0kznr.Mui-disabled{color:rgba(0, 0, 0, 0.26);}.css-q0kznr::before{content:"";position:absolute;width:100%;height:100%;top:-1px;left:-1px;z-index:0;opacity:0;-webkit-transition:opacity 100ms ease-in-out,background-position 400ms ease-in-out;transition:opacity 100ms ease-in-out,background-position 400ms 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0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;transition:background-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,box-shadow 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,border-color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms,color 250ms cubic-bezier(0.4, 0, 0.2, 1) 0ms;color:#00E062;min-width:0;text-transform:capitalize;font-weight:600;border-radius:4px;font-size:1rem;padding-left:2rem;padding-right:2rem;-webkit-transition:unset;transition:unset;white-space:nowrap;position:relative;font-size:1rem;line-height:2;padding-left:1.25rem;padding-right:1.25rem;color:#79AFFA;padding:0;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}.css-ak4akz::-moz-focus-inner{border-style:none;}.css-ak4akz.Mui-disabled{pointer-events:none;cursor:default;}@media 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dsCZKx">Autoencoder</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/accuracy" class="sc-e69ac761-0 dsCZKx">Accuracy in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-detection" class="sc-e69ac761-0 dsCZKx">AI Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-robustness" class="sc-e69ac761-0 dsCZKx">AI Robustness</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-safety" class="sc-e69ac761-0 dsCZKx">AI Safety</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-scalability" class="sc-e69ac761-0 dsCZKx">AI Scalability</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-simulation" class="sc-e69ac761-0 dsCZKx">AI Simulation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-standards" class="sc-e69ac761-0 dsCZKx">AI Standards</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-steering" class="sc-e69ac761-0 dsCZKx">AI Steering</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ai-transparency" class="sc-e69ac761-0 dsCZKx">AI Transparency</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/augmented-intelligence" class="sc-e69ac761-0 dsCZKx">Augmented Intelligence</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/applications" class="sc-e69ac761-0 dsCZKx">Applications</a></li><li data-letter="B" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">B</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/benchmarking" class="sc-e69ac761-0 dsCZKx">Benchmarking</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/batch-gradient-descent" class="sc-e69ac761-0 dsCZKx">Batch Gradient Descent</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/backpropagation" class="sc-e69ac761-0 dsCZKx">Backpropagation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/bayesian-machine-learning" class="sc-e69ac761-0 dsCZKx">Bayesian Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/bert" class="sc-e69ac761-0 dsCZKx">BERT</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/binary-classification-ai" class="sc-e69ac761-0 dsCZKx">Binary Classification AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/beam-search-algorithm" class="sc-e69ac761-0 dsCZKx">Beam Search Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/bias-variance-tradeoff" class="sc-e69ac761-0 dsCZKx">Bias-Variance Tradeoff</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/boosting" class="sc-e69ac761-0 dsCZKx">Boosting in Machine Learning</a></li><li data-letter="C" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">C</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/chess-bots" class="sc-e69ac761-0 dsCZKx">Chess bots</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/chatgpt" class="sc-e69ac761-0 dsCZKx">ChatGPT</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cure-algorithm" class="sc-e69ac761-0 dsCZKx">CURE Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/curse-of-dimensionality" class="sc-e69ac761-0 dsCZKx">Curse of Dimensionality</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/classification" class="sc-e69ac761-0 dsCZKx">Classification</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-map" class="sc-e69ac761-0 dsCZKx">Cognitive Map</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/central-processing-unit-cpu" class="sc-e69ac761-0 dsCZKx">Central Processing Unit (CPU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/conditional-variational-autoencoders" class="sc-e69ac761-0 dsCZKx">Conditional Variational Autoencoders</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/conversational-ai" class="sc-e69ac761-0 dsCZKx">Conversational AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/causal-inference" class="sc-e69ac761-0 dsCZKx">Causal Inference</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/capsule-neural-network" class="sc-e69ac761-0 dsCZKx">Capsule Neural Network</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/contrastive-learning" class="sc-e69ac761-0 dsCZKx">Contrastive Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/convolutional-neural-networks" class="sc-e69ac761-0 dsCZKx">Convolutional Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-computing" class="sc-e69ac761-0 dsCZKx">Cognitive Computing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/common-crawl-datasets" class="sc-e69ac761-0 dsCZKx">Common Crawl Datasets</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/clustering-algorithms" class="sc-e69ac761-0 dsCZKx">Clustering Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/concatenative-synthesis" class="sc-e69ac761-0 dsCZKx">Concatenative Synthesis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/candidate-sampling" class="sc-e69ac761-0 dsCZKx">Candidate Sampling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-creativity" class="sc-e69ac761-0 dsCZKx">Computational Creativity</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/context-aware-computing" class="sc-e69ac761-0 dsCZKx">Context-Aware Computing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/counterfactual-explanations-in-ai" class="sc-e69ac761-0 dsCZKx">Counterfactual Explanations in AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cognitive-architectures" class="sc-e69ac761-0 dsCZKx">Cognitive Architectures</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-phenotyping" class="sc-e69ac761-0 dsCZKx">Computational Phenotyping</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/continuous-learning-systems" class="sc-e69ac761-0 dsCZKx">Continuous Learning Systems</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/chatbots" class="sc-e69ac761-0 dsCZKx">Chatbots</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/composite-ai" class="sc-e69ac761-0 dsCZKx">Composite AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-lingustics" class="sc-e69ac761-0 dsCZKx">Computational Linguistics</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/computational-semantics" class="sc-e69ac761-0 dsCZKx">Computational Semantics</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/collaborative-filtering" class="sc-e69ac761-0 dsCZKx">Collaborative Filtering</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/corpus" class="sc-e69ac761-0 dsCZKx">Corpus in NLP</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/confirmation-bias" class="sc-e69ac761-0 dsCZKx">Confirmation Bias in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/confidence-intervals" class="sc-e69ac761-0 dsCZKx">Confidence Intervals in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/cross-validation" class="sc-e69ac761-0 dsCZKx">Cross Validation in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/clustering" class="sc-e69ac761-0 dsCZKx">Clustering in Machine Learning</a></li><li data-letter="D" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 fvIpti">D</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/dall-e" class="sc-e69ac761-0 dsCZKx">Dall-E</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/distilbert" class="sc-e69ac761-0 dsCZKx">DistilBERT</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/dimensionality-reduction" class="sc-e69ac761-0 dsCZKx">Dimensionality Reduction</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/deep-reinforcement-learning" class="sc-e69ac761-0 dsCZKx">Deep Reinforcement Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/diffusion-model" class="sc-e69ac761-0 dsCZKx">Diffusion Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/deep-learning" class="sc-e69ac761-0 dsCZKx">Deep Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/datasets" class="sc-e69ac761-0 dsCZKx">Datasets</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-labeling" class="sc-e69ac761-0 dsCZKx">Data Labeling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/differential-privacy" class="sc-e69ac761-0 dsCZKx">Differential Privacy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-poisoning" class="sc-e69ac761-0 dsCZKx">Data Poisoning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/domain-adaptation" class="sc-e69ac761-0 dsCZKx">Domain Adaptation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-augmentation" class="sc-e69ac761-0 dsCZKx">Data Augmentation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/double-descent" class="sc-e69ac761-0 ezFGlW">Double Descent</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/deepfake-detection" class="sc-e69ac761-0 dsCZKx">Deepfake Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/diffusion" class="sc-e69ac761-0 dsCZKx">Diffusion</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-drift" class="sc-e69ac761-0 dsCZKx">Data Drift</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/data-scarcity" class="sc-e69ac761-0 dsCZKx">Data Scarcity</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/decision-tree" class="sc-e69ac761-0 dsCZKx">Decision Tree</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/decision-intelligence" class="sc-e69ac761-0 dsCZKx">Decision Intelligence</a></li><li data-letter="E" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">E</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/expectation-maximization" class="sc-e69ac761-0 dsCZKx">Expectation Maximization</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/embedding-layer" class="sc-e69ac761-0 dsCZKx">Embedding Layer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/evolutionary-algorithms" class="sc-e69ac761-0 dsCZKx">Evolutionary Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/explainable-ai" class="sc-e69ac761-0 dsCZKx">Explainable AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/end-to-end-learning" class="sc-e69ac761-0 dsCZKx">End-to-end Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/emergent-behavior" class="sc-e69ac761-0 dsCZKx">Emergent Behavior</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ego-4d" class="sc-e69ac761-0 dsCZKx">Ego 4D</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/eco-friendly-ai" class="sc-e69ac761-0 dsCZKx">Eco-friendly AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ensemble-learning" class="sc-e69ac761-0 dsCZKx">Ensemble Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/entropy" class="sc-e69ac761-0 dsCZKx">Entropy in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/epoch" class="sc-e69ac761-0 dsCZKx">Epoch in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ethical-ai" class="sc-e69ac761-0 dsCZKx">Ethical AI</a></li><li data-letter="F" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">F</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/flajolet-martin-algorithm" class="sc-e69ac761-0 dsCZKx">Flajolet-Martin Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feedforward-neural-network" class="sc-e69ac761-0 dsCZKx">Feedforward Neural Network</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/fine-tuning-deep-learning" class="sc-e69ac761-0 dsCZKx">Fine Tuning in Deep Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/fundamentals" class="sc-e69ac761-0 dsCZKx">Fundamentals</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/f1-score-machine-learning" class="sc-e69ac761-0 dsCZKx">F1 Score in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/foundation-models" class="sc-e69ac761-0 dsCZKx">Foundation Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/forward-propagation" class="sc-e69ac761-0 dsCZKx">Forward Propagation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/f2-score" class="sc-e69ac761-0 dsCZKx">F2 Score</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feature-store-for-machine-learning" class="sc-e69ac761-0 dsCZKx">Feature Store for Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/few-shot-learning" class="sc-e69ac761-0 dsCZKx">Few Shot Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/federated-learning" class="sc-e69ac761-0 dsCZKx">Federated Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feature-learning" class="sc-e69ac761-0 dsCZKx">Feature Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/feature-selection" class="sc-e69ac761-0 dsCZKx">Feature Selection</a></li><li data-letter="G" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">G</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gradient-clipping" class="sc-e69ac761-0 dsCZKx">Gradient Clipping</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/generative-adversarial-networks" class="sc-e69ac761-0 dsCZKx">Generative Adversarial Networks (GANs)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gaussian-processes" class="sc-e69ac761-0 dsCZKx">Gaussian Processes</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gated-recurrent-unit" class="sc-e69ac761-0 dsCZKx">Gated Recurrent Unit</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/grounding" class="sc-e69ac761-0 dsCZKx">Grounding</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gradient-boosting-machines" class="sc-e69ac761-0 dsCZKx">Gradient Boosting Machines (GBMs)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/graphics-processing-unit-gpu" class="sc-e69ac761-0 dsCZKx">Graphics Processing Unit (GPU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/google-bard" class="sc-e69ac761-0 dsCZKx">Google's Bard</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/gradient-scaling" class="sc-e69ac761-0 dsCZKx">Gradient Scaling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/generative-ai" class="sc-e69ac761-0 dsCZKx">Generative AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/graph-neural-networks" class="sc-e69ac761-0 dsCZKx">Graph Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/grapheme-to-phoneme-conversion-g2p" class="sc-e69ac761-0 dsCZKx">Grapheme-to-Phoneme Conversion (G2P)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/generative-teaching-networks" class="sc-e69ac761-0 dsCZKx">Generative Teaching Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/genetic-algorithms" class="sc-e69ac761-0 dsCZKx">Genetic Algorithms in AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/ground-truth" class="sc-e69ac761-0 dsCZKx">Ground Truth in Machine Learning</a></li><li data-letter="H" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">H</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hyperparameters" class="sc-e69ac761-0 dsCZKx">Hyperparameters</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hidden-markov-models" class="sc-e69ac761-0 dsCZKx">Hidden Markov Models (HMMs)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hooke-jeeves-algorithm" class="sc-e69ac761-0 dsCZKx">Hooke-Jeeves Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hyperparameter-tuning" class="sc-e69ac761-0 dsCZKx">Hyperparameter Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/homograph-disambiguation" class="sc-e69ac761-0 dsCZKx">Homograph Disambiguation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/human-centered-ai" class="sc-e69ac761-0 dsCZKx">Human-centered AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hidden-layer" class="sc-e69ac761-0 dsCZKx">Hidden Layer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/human-in-the-loop-ai" class="sc-e69ac761-0 dsCZKx">Human-in-the-Loop AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/hybrid-ai" class="sc-e69ac761-0 dsCZKx">Hybrid AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/human-augmentation-with-ai" class="sc-e69ac761-0 dsCZKx">Human Augmentation with AI</a></li><li data-letter="I" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">I</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/inference-engine" class="sc-e69ac761-0 dsCZKx">Inference Engine</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/intelligent-document-processing" class="sc-e69ac761-0 dsCZKx">Intelligent Document Processing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/imbalanced-data" class="sc-e69ac761-0 dsCZKx">Imbalanced Data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/instruction-tuning" class="sc-e69ac761-0 dsCZKx">Instruction Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/incremental-learning" class="sc-e69ac761-0 dsCZKx">Incremental Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/information-retrieval" class="sc-e69ac761-0 dsCZKx">Information Retrieval</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/image-recognition" class="sc-e69ac761-0 dsCZKx">Image Recognition</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/imagenet" class="sc-e69ac761-0 dsCZKx">ImageNet</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/inductive-bias" class="sc-e69ac761-0 dsCZKx">Inductive Bias</a></li><li data-letter="K" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">K</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/k-shingles" class="sc-e69ac761-0 dsCZKx">k-Shingles</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/keyphrase-extraction" class="sc-e69ac761-0 dsCZKx">Keyphrase Extraction</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/keras" class="sc-e69ac761-0 dsCZKx">Keras</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/knowledge-distillation" class="sc-e69ac761-0 dsCZKx">Knowledge Distillation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/knowledge-representation-and-reasoning" class="sc-e69ac761-0 dsCZKx">Knowledge Representation and Reasoning</a></li><li data-letter="L" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">L</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/llama-2" class="sc-e69ac761-0 dsCZKx">Llama 2</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/llm-collection" class="sc-e69ac761-0 dsCZKx">LLM Collection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/latent-dirichlet-allocation" class="sc-e69ac761-0 dsCZKx">Latent Dirichlet Allocation (LDA)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/large-language-model" class="sc-e69ac761-0 dsCZKx">Large Language Model (LLM)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/loss-function" class="sc-e69ac761-0 dsCZKx">Loss Function</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/limited-memory-ai" class="sc-e69ac761-0 dsCZKx">Limited Memory AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/learning-rate" class="sc-e69ac761-0 dsCZKx">Learning Rate</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/learning-to-rank" class="sc-e69ac761-0 dsCZKx">Learning To Rank</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/logits" class="sc-e69ac761-0 dsCZKx">Logits</a></li><li data-letter="M" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">M</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/midjourney-image-generation" class="sc-e69ac761-0 dsCZKx">Midjourney (Image Generation)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/mistral" class="sc-e69ac761-0 dsCZKx">Mistral</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/mixture-of-experts" class="sc-e69ac761-0 dsCZKx">Mixture of Experts</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multimodal-ai" class="sc-e69ac761-0 dsCZKx">Multimodal AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multimodal-learning" class="sc-e69ac761-0 dsCZKx">Multimodal Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning" class="sc-e69ac761-0 dsCZKx">Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multimodal-aI-models-and-modalities" class="sc-e69ac761-0 dsCZKx">Multimodal AI Models and Modalities</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/mamba" class="sc-e69ac761-0 dsCZKx">Mamba</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/models" class="sc-e69ac761-0 dsCZKx">Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-bias" class="sc-e69ac761-0 dsCZKx">Machine Learning Bias</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-life-cycle-management" class="sc-e69ac761-0 dsCZKx">Machine Learning Life Cycle Management</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-translation" class="sc-e69ac761-0 dsCZKx">Machine Translation</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/mlops" class="sc-e69ac761-0 dsCZKx">MLOps</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/monte-carlo-learning" class="sc-e69ac761-0 dsCZKx">Monte Carlo Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multi-task-learning" class="sc-e69ac761-0 dsCZKx">Multi-task Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-neuron" class="sc-e69ac761-0 dsCZKx">Machine Learning Neuron</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-preprocessing" class="sc-e69ac761-0 dsCZKx">Machine Learning Preprocessing</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/model-drift" class="sc-e69ac761-0 dsCZKx">Model Drift</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/matplotlib" class="sc-e69ac761-0 dsCZKx">Matplotlib</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/Markov-decision-process" class="sc-e69ac761-0 dsCZKx">Markov Decision Process</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/model-interpretability" class="sc-e69ac761-0 dsCZKx">Model Interpretability</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/machine-learning-algorithmic-trading" class="sc-e69ac761-0 dsCZKx">Machine Learning in Algorithmic Trading</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/metacognitive-learning-models" class="sc-e69ac761-0 dsCZKx">Metacognitive Learning Models </a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/metaheuristic-algorithms" class="sc-e69ac761-0 dsCZKx">Metaheuristic Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multitask-prompt-tuning" class="sc-e69ac761-0 dsCZKx">Multitask Prompt Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/multi-agent-systems" class="sc-e69ac761-0 dsCZKx">Multi-Agent Systems</a></li><li data-letter="N" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">N</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-processing" class="sc-e69ac761-0 dsCZKx">Natural Language Processing (NLP)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-generation" class="sc-e69ac761-0 dsCZKx">Natural Language Generation (NLG)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-understanding" class="sc-e69ac761-0 dsCZKx">Natural Language Understanding (NLU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neuralink" class="sc-e69ac761-0 dsCZKx">Neuralink</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/naive-bayes-classifier" class="sc-e69ac761-0 dsCZKx">Naive Bayes Classifier</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-radiance-fields" class="sc-e69ac761-0 dsCZKx">Neural Radiance Fields</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-querying" class="sc-e69ac761-0 dsCZKx">Natural Language Querying (NLQ)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/numpy" class="sc-e69ac761-0 dsCZKx">NumPy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/natural-language-toolkit-nltk" class="sc-e69ac761-0 dsCZKx">Natural Language Toolkit (NLTK)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-architecture-search" class="sc-e69ac761-0 dsCZKx">Neural Architecture Search</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-text-to-speech-ntts" class="sc-e69ac761-0 dsCZKx">Neural Text-to-Speech (NTTS)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/named-entity-recognition" class="sc-e69ac761-0 dsCZKx">Named Entity Recognition</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neural-style-transfer" class="sc-e69ac761-0 dsCZKx">Neural Style Transfer</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/neuroevolution" class="sc-e69ac761-0 dsCZKx">Neuroevolution</a></li><li data-letter="O" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">O</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/online-gradient-descent" class="sc-e69ac761-0 dsCZKx">Online Gradient Descent</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/overfitting-underfitting" class="sc-e69ac761-0 dsCZKx">Overfitting and Underfitting</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/openai-whisper" class="sc-e69ac761-0 dsCZKx">OpenAI Whisper</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/openai-sora" class="sc-e69ac761-0 dsCZKx">OpenAI Sora</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/out-of-distribution-detection" class="sc-e69ac761-0 dsCZKx">Out-of-Distribution Detection</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/one-shot-learning" class="sc-e69ac761-0 dsCZKx">One-Shot Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/objective-function" class="sc-e69ac761-0 dsCZKx">Objective Function</a></li><li data-letter="P" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">P</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/prompt-engineering" class="sc-e69ac761-0 dsCZKx">Prompt Engineering</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/prompt-chaining" class="sc-e69ac761-0 dsCZKx">Prompt Chaining</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/perceptron" class="sc-e69ac761-0 dsCZKx">Perceptron</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/precision-and-recall" class="sc-e69ac761-0 dsCZKx">Precision and Recall</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/packages-glossary" class="sc-e69ac761-0 dsCZKx">Packages</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pooling-machine-learning" class="sc-e69ac761-0 dsCZKx">Pooling (Machine Learning)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/principal-component-analysis" class="sc-e69ac761-0 dsCZKx">Principal Component Analysis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/probabilistic-models-in-machine-learning" class="sc-e69ac761-0 dsCZKx">Probabilistic Models in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/prompt-tuning" class="sc-e69ac761-0 dsCZKx">Prompt Tuning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pytorch" class="sc-e69ac761-0 dsCZKx">PyTorch</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pandas" class="sc-e69ac761-0 dsCZKx">Pandas</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/parametric-neural-networks%C2%A0" class="sc-e69ac761-0 dsCZKx">Parametric Neural Networks </a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/pretraining" class="sc-e69ac761-0 dsCZKx">Pretraining</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/part-of-speech-tagging" class="sc-e69ac761-0 dsCZKx">Part-of-Speech Tagging</a></li><li data-letter="Q" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">Q</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/quantum-machine-learning-algorithms" class="sc-e69ac761-0 dsCZKx">Quantum Machine Learning Algorithms</a></li><li data-letter="R" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">R</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/rule-based-ai" class="sc-e69ac761-0 dsCZKx">Rule-Based AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/roberta" class="sc-e69ac761-0 dsCZKx">RoBERTa</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/rlhf" class="sc-e69ac761-0 dsCZKx">RLHF</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/retrieval-augmented-generation" class="sc-e69ac761-0 dsCZKx">Retrieval-Augmented Generation (RAG)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/representation-learning" class="sc-e69ac761-0 dsCZKx">Representation Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/rectified-linear-unit-relu" class="sc-e69ac761-0 dsCZKx">Rectified Linear Unit (ReLU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/reproducibility-machine-learning" class="sc-e69ac761-0 dsCZKx">Reproducibility in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/restricted-boltzmann-machines" class="sc-e69ac761-0 dsCZKx">Restricted Boltzmann Machines</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/regularization" class="sc-e69ac761-0 dsCZKx">Regularization</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/recurrent-neural-networks" class="sc-e69ac761-0 dsCZKx">Recurrent Neural Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/random-forest" class="sc-e69ac761-0 dsCZKx">Random Forest</a></li><li data-letter="S" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">S</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/sentiment-analysis" class="sc-e69ac761-0 dsCZKx">Sentiment Analysis</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/speech-to-text-models" class="sc-e69ac761-0 dsCZKx">Speech-to-text models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/sequence-modeling" class="sc-e69ac761-0 dsCZKx">Sequence Modeling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semantic-kernel" class="sc-e69ac761-0 dsCZKx">Semantic Kernel</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semi-supervised-learning" class="sc-e69ac761-0 dsCZKx">Semi-Supervised Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/supervised-learning" class="sc-e69ac761-0 dsCZKx">Supervised Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/support-vector-machines-svm" class="sc-e69ac761-0 dsCZKx">Support Vector Machines (SVM)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semantic-networks" class="sc-e69ac761-0 dsCZKx">Semantic Networks</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semi-structured-data" class="sc-e69ac761-0 dsCZKx">Semi-structured data</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/scikit-learn" class="sc-e69ac761-0 dsCZKx">Scikit-learn</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/scipy" class="sc-e69ac761-0 dsCZKx">SciPy</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/seaborn-python-package" class="sc-e69ac761-0 dsCZKx">Seaborn Python Package</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/squad" class="sc-e69ac761-0 dsCZKx">SQuAD</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/synthetic-data-for-ai-training" class="sc-e69ac761-0 dsCZKx">Synthetic Data for AI Training</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/statistical-relational-learning" class="sc-e69ac761-0 dsCZKx">Statistical Relational Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/self-healing-ai" class="sc-e69ac761-0 dsCZKx">Self-healing AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/semantic-search-algorithms" class="sc-e69ac761-0 dsCZKx">Semantic Search Algorithms</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/symbolic-ai" class="sc-e69ac761-0 dsCZKx">Symbolic AI</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/spike-neural-networks" class="sc-e69ac761-0 dsCZKx">Spike Neural Networks</a></li><li data-letter="T" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">T</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/text-to-speech-models" class="sc-e69ac761-0 dsCZKx">Text-to-Speech Models</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/transformers" class="sc-e69ac761-0 dsCZKx">Transformers</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/tensor-processing-unit-tpu" class="sc-e69ac761-0 dsCZKx">Tensor Processing Unit (TPU)</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/tokenization" class="sc-e69ac761-0 dsCZKx">Tokenization</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/techniques" class="sc-e69ac761-0 dsCZKx">Techniques</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/topic-modeling" class="sc-e69ac761-0 dsCZKx">Topic Modeling</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/transfer-learning" class="sc-e69ac761-0 dsCZKx">Transfer Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/tensorflow" class="sc-e69ac761-0 dsCZKx">TensorFlow</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/the-pile" class="sc-e69ac761-0 dsCZKx">The Pile</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/test-data-set" class="sc-e69ac761-0 dsCZKx">Test Data Set</a></li><li data-letter="U" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">U</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/uncertainty-machine-learning" class="sc-e69ac761-0 dsCZKx">Uncertainty in Machine Learning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/unsupervised-learning" class="sc-e69ac761-0 dsCZKx">Unsupervised Learning</a></li><li data-letter="V" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">V</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/vanishing-and-exploding-gradients" class="sc-e69ac761-0 dsCZKx">Vanishing and Exploding Gradients</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/voice-cloning" class="sc-e69ac761-0 dsCZKx">Voice Cloning</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/validation-data-set" class="sc-e69ac761-0 dsCZKx">Validation Data Set</a></li><li data-letter="W" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">W</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/winnow-algorithm" class="sc-e69ac761-0 dsCZKx">Winnow Algorithm</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/word-embeddings" class="sc-e69ac761-0 dsCZKx">Word Embeddings</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/whisper-v3" class="sc-e69ac761-0 dsCZKx">Whisper v3</a><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/whisper-v2" class="sc-e69ac761-0 dsCZKx">Whisper v2</a></li><li data-letter="X" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">X</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/xlnet" class="sc-e69ac761-0 dsCZKx">XLNet</a></li><li data-letter="Z" class="sc-ace17a57-0 eTCxuy"><div width="100%" class="sc-6293d692-0 jWSoNY"><span font-size="textLg" font-weight="medium" class="sc-b323b31-0 jgUCVJ">Z</span></div><a rel="" target="" font-size="textLg" font-weight="medium" href="/ai-glossary/zero-shot-classification-models" class="sc-e69ac761-0 dsCZKx">Zero-shot Classification Models</a></li></nav></div></div></div></div></div></div></div></div></section><section id="blog-conversion-panel-section" width="100%" class="sc-ace17a57-0 sc-b22001da-2 gAaKYn dJJSTR"><div width="100%" class="sc-6293d692-0 hzUpmg"></div></section><footer class="sc-6293d692-0 jUEsCq"><div class="sc-6293d692-0 jBxPcy"><div class="sc-ace17a57-0 kUNxIf"><div width="100%" class="sc-ace17a57-0 kptHGM"><div class="sc-ace17a57-0 djSuqG"><div class="sc-ace17a57-0 sc-acb32398-0 fJkbQy iBHmhe"><div class="sc-ace17a57-0 sc-5f7d928-0 iPwPdJ kritbo image-wrapper" width="100%" height="fit-content"><img alt="Deepgram Logo" loading="lazy" width="172" height="33" decoding="async" data-nimg="1" style="color:transparent;object-fit:cover" src="https://www.datocms-assets.com/96965/1725550993-deepgram-logo.svg"/></div></div><span font-size="textSm" font-weight="regular" 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Deepgram</span></div></div></div></footer></div></div><script id="__NEXT_DATA__" type="application/json">{"props":{"pageProps":{"slug":["double-descent"],"pageData":{"templateGlossary":{"__typename":"TemplateGlossaryRecord","id":"aYvqoTJARsSeQDnXWfTMdQ","seo":null,"slug":"double-descent","title":"Double Descent","categoryPage":false,"excerpt":{"__typename":"TemplateGlossaryModelExcerptField","value":{"schema":"dast","document":{"type":"root","children":[{"type":"paragraph","children":[{"type":"span","value":"This article aims to demystify the concept of double descent in deep learning, providing you with a comprehensive understanding of its implications for model selection and training strategies."}]}]}}},"body":{"__typename":"TemplateGlossaryModelBodyField","blocks":[],"links":[{"__typename":"ComponentImageRecord","id":"NpVOtWPlToearVCrOThlKA","caption":"From virtual TAs to accessibility expansion, [this 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But some data is better than others. [This article](https://deepgram.com/learn/the-ai-echo-chamber-model-collapse-synthetic-data-risks) unveils the unspoken truth of synthetic data.","imageDesktop":{"__typename":"FileField","id":"QU2pq6FHQ4iSD6II6lQvXA","title":null,"filename":"screen-shot-2024-06-18-at-11-48-34-am.png","size":3258631,"alt":null,"url":"https://www.datocms-assets.com/96965/1718736518-screen-shot-2024-06-18-at-11-48-34-am.png","width":1796,"height":1088},"imageMobile":null,"link":""},{"__typename":"ComponentImageRecord","id":"OcUPVLYOTdiOH90vXDPFbA","caption":"Mixture of Experts (MoE) is a method that presents an efficient approach to dramatically increasing a model’s capabilities without introducing a proportional amount of computational overhead. To learn more, check out [this guide](https://deepgram.com/learn/mixture-of-experts-ml-model-guide)!","imageDesktop":{"__typename":"FileField","id":"cnmz5FWiQv2S--QFhqNL-g","title":null,"filename":"screen-shot-2024-06-16-at-2-06-22-am.png","size":2233720,"alt":null,"url":"https://www.datocms-assets.com/96965/1718528786-screen-shot-2024-06-16-at-2-06-22-am.png","width":1512,"height":788},"imageMobile":null,"link":""}],"value":{"schema":"dast","document":{"type":"root","children":[{"type":"paragraph","children":[{"type":"span","value":"Have you ever been intrigued by the way "},{"url":"https://deepgram.com/ai-glossary/deep-learning","type":"link","children":[{"type":"span","value":"deep learning"}]},{"type":"span","value":" models defy conventional wisdom, especially when it comes to model complexity and overfitting? It’s a common challenge for many in the field: the delicate balancing act of increasing model complexity to improve performance, without inadvertently stepping into the realm of overfitting. Recent research, such as the groundbreaking study from arXiv, has brought to light a phenomenon that challenges these traditional beliefs: the concept of double descent. This revelation not only surprises but also reshapes our understanding of overparameterization and generalization error in deep learning."}]},{"type":"paragraph","children":[{"type":"span","value":"This article aims to demystify the concept of double descent in deep learning, providing you with a comprehensive understanding of its implications for model selection and training strategies. By exploring key terms such as overparameterization, generalization error, and the bias-variance tradeoff, we'll delve into how double descent defies the long-held principle of the bias-variance tradeoff. The significance of this phenomenon in explaining the unprecedented success of deep neural networks cannot be overstated. As we set the stage for a deeper dive into the specifics of double descent, ask yourself: how might this insight change the way you approach model complexity in your deep learning projects?"}]},{"type":"heading","level":2,"children":[{"type":"span","marks":["strong"],"value":"Introduction to Double Descent"}]},{"type":"paragraph","children":[{"type":"span","value":"The concept of double descent in deep learning offers an intriguing twist to the narrative of overfitting and model complexity. At its core, double descent describes a phenomenon where increasing the complexity of a model beyond a certain point—contrary to leading to overfitting—actually improves its performance on test data. This challenges the traditional view encapsulated by the bias-variance tradeoff, which suggests that after a certain point, increasing a model's complexity leads to a decrease in its ability to generalize to unseen data. Let's unpack some key aspects of this phenomenon:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Overparameterization: This refers to situations where the number of parameters in a model far exceeds the number of training data points. Surprisingly, models in the highly overparameterized regime can achieve better test error rates, a finding supported by a study on arXiv."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Generalization Error: The discrepancy between a model's performance on training data and unseen data. The double descent curve reveals that generalization error decreases, increases, and then decreases again as model complexity grows, painting a complex picture of how deep learning models learn."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Bias-Variance Tradeoff: Historically, the bias-variance tradeoff has been a guiding principle in understanding the relationship between model complexity and generalization error. However, the existence of double descent suggests that this tradeoff does not fully capture the dynamics at play in deep learning models."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"The discovery of double descent challenges us to rethink model selection and training strategies in deep learning. It underscores the importance of exploring models in the highly overparameterized regime and offers a fresh perspective on why deep neural networks have achieved remarkable success across a range of applications. As we proceed, we delve deeper into the mechanics of double descent in the context of deep learning models, exploring its implications through examples from recent studies and discussing its impact on training strategies."}]},{"type":"heading","level":2,"children":[{"type":"span","marks":["strong"],"value":"Double Descent in Deep Learning Models"}]},{"type":"paragraph","children":[{"type":"span","value":"The journey through the landscape of deep learning models reveals an intriguing phenomenon known as double descent. This phenomenon, observed in the behavior of two-layer neural networks among others, provides a novel perspective on model complexity and its impact on test error rates. Let's explore the mechanics and implications of this phenomenon in detail."}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"The Mechanics of Double Descent"}]},{"type":"paragraph","children":[{"type":"span","value":"Double descent occurs in a three-phase process:"}]},{"type":"list","style":"numbered","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Underfitting Phase: As the complexity of a deep learning model begins to increase, the test error decreases. This phase is characterized by models that are not complex enough to capture the underlying patterns in the data, leading to high bias."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Overfitting Phase: Continuing to add complexity to the model leads to an increase in test error. During this phase, models are too complex relative to the amount of training data, capturing noise as if it were signal, which results in high variance."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Second Descent: Remarkably, as model complexity grows even further, entering the highly overparameterized regime, the test error begins to decrease once again. This counterintuitive phase defies traditional expectations about overfitting."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Examples from Recent Studies"}]},{"type":"paragraph","children":[{"type":"span","value":"Recent research has illuminated the occurrence of double descent across various deep learning architectures:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Convolutional Neural Networks (CNNs), Residual Networks (ResNets), and Transformers have all demonstrated this phenomenon, as highlighted by OpenAI's research on deep double descent. These architectures initially exhibit decreased test error, encounter a peak of increased error, and then surprisingly show a decline in error as model complexity continues to grow."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"The role of model parameters and the ratio of parameters to data points is crucial in triggering double descent. Models with a high parameter-to-data point ratio enter the overparameterized regime, where the second descent becomes observable."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"The Implications of Double Descent"}]},{"type":"paragraph","children":[{"type":"span","value":"Understanding double descent has significant implications for the design and training of deep learning models:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"It challenges the conventional wisdom that there is a straightforward trade-off between bias and variance as model complexity increases."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"The phenomenon suggests that in certain cases, increasing model size could lead to better generalization, even in the absence of additional data."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"This insight informs the choice of model size, encouraging practitioners to consider highly overparameterized models as viable and potentially optimal choices for certain tasks."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Epoch-wise Double Descent"}]},{"type":"paragraph","children":[{"type":"span","value":"Not limited to model complexity, double descent also manifests across training epochs:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"As discussed in a study on arXiv, epoch-wise double descent occurs at specific noise levels and parameter values. The phenomenon is observed when training for an extended number of epochs, showcasing a similar pattern of test error reduction after an initial increase."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"This suggests that not only the architecture and size of the model but also the duration of training and the presence of noise in the data can influence the occurrence of double descent."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"Double descent offers a nuanced view of the relationship between model complexity and generalization in deep learning. It underscores the importance of exploring a wider range of model architectures and sizes, as well as training durations, to fully leverage the potential of deep neural networks. The phenomenon of double descent, with its surprising second descent in test error, challenges long-held beliefs and opens new avenues for research and application in the field of deep learning."}]},{"type":"paragraph","children":[{"item":"NpVOtWPlToearVCrOThlKA","type":"inlineItem"}]},{"type":"heading","level":2,"children":[{"type":"span","marks":["strong"],"value":"The Impact of Double Descent on Training"}]},{"type":"paragraph","children":[{"type":"span","value":"The phenomenon of double descent significantly influences training strategies and outcomes in deep learning. As we navigate this complex landscape, understanding its impact enables us to refine our approaches to model selection, training duration, and data management."}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Navigating the Double Descent Curve"}]},{"type":"paragraph","children":[{"type":"span","value":"Strategising around the double descent curve involves several key considerations:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Model Size Selection: The perplexing nature of double descent necessitates a departure from traditional model selection strategies. Instead of avoiding overparameterization, embracing larger models may lead to better generalization in the regime beyond the double descent peak. This counterintuitive approach requires careful experimentation to identify the optimal model size that leverages the second descent for improved test error rates."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Training Duration: The occurrence of epoch-wise double descent suggests that the duration of training also plays a critical role. Extending training beyond the point where overfitting typically occurs can unexpectedly reduce test errors. However, this demands precise control and monitoring to avoid excessive training that may not yield further improvements."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Data Management: In the face of double descent, the importance of data quality and quantity becomes even more pronounced. Highly overparameterized models have an insatiable appetite for data, making the acquisition of larger, high-quality datasets a priority. Simultaneously, data preprocessing and augmentation techniques gain importance to maximize the utility of available data."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Implications for Early Stopping and Regularization"}]},{"type":"paragraph","children":[{"type":"span","value":"Double descent reshapes the landscape of model training techniques:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Early Stopping: The traditional practice of early stopping to prevent overfitting must be revisited. Given the potential benefits of navigating past the overfitting peak into the second descent, determining the optimal stopping point becomes more nuanced. Experimentation and validation against a holdout dataset are crucial to identify when further training ceases to yield benefits."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Regularization Techniques: While regularization remains a cornerstone of combating overfitting, its role is nuanced in the context of double descent. Techniques such as dropout or weight decay must be applied judiciously, balancing the need to prevent overfitting against the possibility of hindering the model's journey into the beneficial overparameterized regime."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Leveraging Insights from the Machine Learning Community"}]},{"type":"paragraph","children":[{"type":"span","value":"The "},{"url":"https://deepgram.com/ai-glossary/machine-learning","type":"link","children":[{"type":"span","value":"machine learning"}]},{"type":"span","value":" community provides valuable insights into managing double descent:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Luca Massaron's Advice: In his exploration of deep learning for tabular data, Luca Massaron emphasizes the challenges posed by sparse data and the lack of best practice architectures. His recommendation to use regularization techniques like L1/L2 and dropout, alongside feature engineering, offers a roadmap for navigating double descent in practical applications."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Architectural Considerations: The choice of neural architecture plays a pivotal role in mitigating the impacts of double descent. Specific architectures, informed by the latest research and community insights, can be more resilient to the pitfalls of overparameterization. Experimentation with different configurations and adherence to best practices are key to harnessing the benefits of double descent."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Identifying the Optimal Stopping Point"}]},{"type":"paragraph","children":[{"type":"span","value":"One of the most daunting challenges in the era of double descent is pinpointing the optimal moment to halt model training. This decision requires a delicate balance, aiming to maximize generalization without succumbing to the detrimental effects of overfitting. Rigorous validation, coupled with an awareness of the double descent phenomenon, guides this critical decision-making process."}]},{"type":"paragraph","children":[{"type":"span","value":"The journey through the double descent phenomenon in deep learning is complex and fraught with counterintuitive insights. However, armed with a deep understanding of its mechanics and implications, practitioners can navigate this landscape more effectively, optimizing their models for superior performance and generalization."}]},{"type":"paragraph","children":[{"item":"AGJOfobER-azW9kVyt5ZiA","type":"inlineItem"}]},{"type":"heading","level":2,"children":[{"type":"span","marks":["strong"],"value":"Identifying and Interpreting Double Descent"}]},{"type":"paragraph","children":[{"type":"span","value":"The double descent phenomenon in deep learning, while initially counterintuitive, has profound implications on how we approach model training and complexity. Understanding and identifying this phenomenon is not just an academic exercise but a practical necessity for improving model performance. This section delves into the methodologies for spotting double descent, the tools at our disposal, and real-world implications, providing a comprehensive guide for practitioners."}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Methods for Plotting and Analyzing Test Error"}]},{"type":"paragraph","children":[{"type":"span","value":"Identifying the double descent curve requires meticulous analysis of test error as a function of model complexity or training epochs. Here's how:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Plotting Test Error vs. Model Complexity: Start by incrementally increasing the model's complexity, plotting the test error at each step. The initial decrease, subsequent increase, and eventual second decrease in test error illustrate the double descent curve. Tools like Matplotlib or Seaborn in Python are instrumental for this visualization."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Analyzing Error over Training Epochs: Similarly, plotting test error as a function of training epochs can reveal an epoch-wise double descent. This requires tracking test errors across training epochs, a task for which deep learning frameworks like TensorFlow or PyTorch are well-suited."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Tools and Libraries for Visualization"}]},{"type":"paragraph","children":[{"type":"span","value":"Several tools and libraries can aid in visualizing the double descent phenomenon:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Python Libraries: Utilize Matplotlib, Seaborn, or Plotly for creating comprehensive plots that clearly illustrate the double descent curve. These libraries offer flexibility in data visualization, allowing for detailed analysis."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Deep Learning Frameworks: TensorFlow and PyTorch not only facilitate model training but also provide utilities for monitoring training progress, including test errors, which are crucial for identifying double descent."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Understanding Data Distribution and Model Assumptions"}]},{"type":"paragraph","children":[{"type":"span","value":"A deep understanding of the underlying data distribution and model assumptions is essential when interpreting double descent:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Data Distribution: Recognize that the double descent phenomenon is influenced by the data's characteristics, including its distribution and noise level. Anomalies in data can significantly impact the model's learning curve and test errors."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Model Assumptions: Each model comes with its set of assumptions about the data it's learning from. When identifying double descent, consider how these assumptions interact with the data's actual characteristics."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Real-World Applications and Case Studies"}]},{"type":"paragraph","children":[{"type":"span","value":"Double descent has been observed and addressed in various real-world applications, offering valuable insights:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Image Classification: In tasks like image classification, researchers have documented the double descent phenomenon across different architectures, including CNNs and ResNets. These case studies provide practical examples of double descent in action, highlighting the significance of model complexity and training strategy adjustments."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"url":"https://deepgram.com/ai-glossary/natural-language-processing","type":"link","children":[{"type":"span","value":"Natural Language Processing (NLP)"}]},{"type":"span","value":": Similarly, in NLP tasks, models like transformers have exhibited double descent behavior, underscoring the importance of data management and model selection strategies tailored to this phenomenon."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Mathematical Explanation for Double Descent"}]},{"type":"paragraph","children":[{"type":"span","value":"A deeper understanding of double descent comes from diving into its mathematical foundations:"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Prediction Risk and Overparameterization: The mathematical explanation for double descent, as discussed on naologic.com, delineates how overparameterization—having more parameters in the model than data points—leads to a reduction in prediction risk after an initial increase. This elucidates why larger models can, paradoxically, generalize better in certain regimes."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Bias-Variance Tradeoff Revisited: Double descent offers a new perspective on the bias-variance tradeoff, highlighting scenarios where traditional models of this tradeoff do not apply. Understanding the mathematical underpinnings of double descent provides a theoretical basis for its practical observations."}]}]}]},{"type":"paragraph","children":[{"type":"span","value":"Identifying and interpreting double descent requires a blend of visualization techniques, a solid grasp of the underlying data and model dynamics, and an appreciation of its mathematical basis. By leveraging these insights, practitioners can better navigate the complexities of model training in the era of deep learning, optimizing their approaches for improved performance and generalization."}]},{"type":"heading","level":2,"children":[{"type":"span","marks":["strong"],"value":"Double Descent and the Bias-Variance Tradeoff"}]},{"type":"paragraph","children":[{"type":"span","value":"The bias-variance tradeoff has long stood as a cornerstone principle in the realm of machine learning, guiding practitioners in their quest for the optimal balance between model simplicity and complexity. However, the discovery of the double descent phenomenon has cast this traditional model into a new light, suggesting there are realms of model behavior previously unaccounted for."}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"A New Perspective on Model Error Decomposition"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Challenging Traditional Models: Double descent reveals that increasing model complexity beyond a certain point can actually lead to improved test error rates, challenging the traditional view where increasing complexity indefinitely leads to overfitting."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Evidence of Model-Wise and Epoch-Wise Regimes: Unlike the classical bias-variance tradeoff, which suggests a monotonous relationship between model complexity and error, double descent indicates the existence of distinct phases or regimes in the training process. This includes both model-wise regimes, where increasing the number of parameters can lead to better performance, and epoch-wise regimes, where training duration also impacts error rates in non-linear ways."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Theoretical Implications for Deep Learning Models"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Beyond Overfitting: The phenomenon provides concrete evidence that the capacity of deep learning models to generalize cannot solely be explained through the lens of overfitting. This has profound implications for how we understand model training and generalization."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Mikhail Belkin’s Contribution: Mikhail Belkin's work, referenced in the Communications of the ACM, has been pivotal in shedding light on the double descent phenomenon. His research underscores the complexity of learning dynamics in highly overparameterized models and the need to rethink generalization in this context."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Double Descent: Challenge or Complement to Bias-Variance?"}]},{"type":"list","style":"bulleted","children":[{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"A Complementary Perspective: While double descent appears to challenge the traditional bias-variance tradeoff, it might also be seen as a complement, expanding our understanding of model behavior in highly parameterized regimes. It suggests that the bias-variance tradeoff is not obsolete but rather incomplete, lacking in its accounting for modern deep learning architectures."}]}]},{"type":"listItem","children":[{"type":"paragraph","children":[{"type":"span","value":"Implications for Model Selection: The acknowledgment of double descent necessitates a more nuanced approach to model selection and training strategy. It implies that the path to optimal model performance is not simply a matter of minimizing complexity but may involve embracing and navigating through phases of increased complexity."}]}]}]},{"type":"heading","level":3,"children":[{"type":"span","marks":["strong"],"value":"Future Research Directions"}]},{"type":"paragraph","children":[{"type":"span","value":"The exploration of double descent opens up new avenues for research, particularly in the study of deep learning models' generalization capabilities. 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